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Phys. Sci. Forum, 2021, ECU 2021

The 1st Electronic Conference on Universe

Online | 22–28 February 2021

Volume Editor:
Lorenzo Iorio, dell' Università e della Ricerca (M.I.U.R.)-Istruzione, Italy

Number of Papers: 62
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Cover Story (view full-size image): Universe 2021: 1st Electronic Conference on Gravitation, Cosmology, Field Theory, High Energy Physics, and Astronomy, was held from 22 to 28 February 2021, which enabled scholars to share and discuss [...] Read more.
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162 KiB  
Abstract
Interactive Applications to Teach the Einstein’s Energy-Momentum-Mass Relation in the Secondary School
by Lorenzo Galante
Phys. Sci. Forum 2021, 2(1), 1; https://doi.org/10.3390/ECU2021-09324 - 22 Feb 2021
Viewed by 1388
Abstract
Two Geogebra-based interactive applications to teach the Special Relativity Energy-Mass-Momentum relation are presented. They are useful tools to visualise the mathematical relation from a geometrical perspective, thus helping students facing calculus difficulties to understand the beauty of this equation. Both give students the [...] Read more.
Two Geogebra-based interactive applications to teach the Special Relativity Energy-Mass-Momentum relation are presented. They are useful tools to visualise the mathematical relation from a geometrical perspective, thus helping students facing calculus difficulties to understand the beauty of this equation. Both give students the opportunity to carry out explorations and come to conclusions. Students are asked to inquire the meaning of the p/E ratio for particles with different masses and energies, to discover that a system with a given finite mass and increasing energy travels at a speed approaching a finite value. Even the relativistic meaning of the mass of a system two particles can be addressed. Students can discover that the relativistic mass is different from the mere sum of the masses of the system, is always greater than or equal to the sum of the masses, depends on the momenta directions and is equal to the sum of the masses if all the particles of the system are at rest. As these concepts are crucial for the understanding of how particles are discovered in Particle Physics, the two applications open the way to introduce students to the main aspects of modern research in Nuclear and Accelerators Physics. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
176 KiB  
Abstract
Multimessenger Probes for New Physics in the Light of A. Sakharov’s Legacy in Cosmoparticle Physics
by Maxim Yu. Khlopov
Phys. Sci. Forum 2021, 2(1), 2; https://doi.org/10.3390/ECU2021-09271 - 22 Feb 2021
Viewed by 1087
Abstract
The modern, standard cosmological scenario, which reflects, to a large extent, the development of A. D. Sakharov’s legacy in cosmoparticle physics, involves inflation, baryosynthesis and dark matter/energy. The physics of all these elements of the cosmological paradigm lays beyond the standard model (BSM) [...] Read more.
The modern, standard cosmological scenario, which reflects, to a large extent, the development of A. D. Sakharov’s legacy in cosmoparticle physics, involves inflation, baryosynthesis and dark matter/energy. The physics of all these elements of the cosmological paradigm lays beyond the standard model (BSM) of elementary particles and involves, in its turn, cosmological probes for its study. To specify this physics, the idea of multimessenger probes of new physics is proposed, involving the set of additional model-dependent consequences of physical models for inflation, baryosynthesis and dark matter. After brief review of the cosmophenomenology of new physics, we concentrate on probes for mechanisms of baryosynthesis—first proposed by A. D. Sakharov—which are of special interest in this context. Antimatter domains formed in the early universe can reflect possible strong nonhomogeneity of baryosynthesis. In the homogeneous and isotropic universe, such nonhomogeneity is determined by specific model-dependent choices of mechanisms of inflation and baryosynthesis. These mechanisms provide tests for the physics, underlying modern cosmology. Constraints on macroscopic antimatter objects or cosmic fluxes of antinuclei provide probes for the corresponding models. Positive evidence for macroscopic antimatter existence leads beyond the standard paradigm of the cosmological scenario and specifies with high precision the parameters of BSM physics. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
154 KiB  
Abstract
Can an Extra Dimension Pull Space-Time?
by Vijay Singh and Aroonkumar Beesham
Phys. Sci. Forum 2021, 2(1), 4; https://doi.org/10.3390/ECU2021-09518 - 19 Mar 2021
Viewed by 1434
Abstract
Over the years, efforts to unify gravity with other fundamental forces in nature has been an active field of research. Looking for the common origin of fundamental interactions, one may arrive at Kaluza–Klein type theories. Generalized Kaluza–Klein models offer an attractive possibility of [...] Read more.
Over the years, efforts to unify gravity with other fundamental forces in nature has been an active field of research. Looking for the common origin of fundamental interactions, one may arrive at Kaluza–Klein type theories. Generalized Kaluza–Klein models offer an attractive possibility of unifying gravity with the other fundamental forces aiming at the extension of space–time from 4D to higher “mathematical” dimensions. In this paper, a generalization of the standard class of exact solutions in Kaluza–Klein (4 + 1) gravity are obtained for a homogeneous cosmological model filled with vacuum energy. In the algebraic and physical sense, these solutions generalize the previously found solutions in the literature. A unified and systematic treatment by solving the field equations in a straight forward manner is more appealing. The deceleration parameter shows that the model exhibits a transition from a decelerated to an accelerated universe. Recent observations have generated strong theoretical and observational evidence that the present expansion of the universe is in an accelerated phase. There is also observational evidence that beyond a certain value of redshift, the universe has been undergoing decelerated expansion. The models which describe transition from a decelerated to an accelerated phase are in the line of observational outcomes and of physical interest. The standard three-space expands indefinitely. Extra dimensions exhibit contraction as well as expansion with suitable values of the parameters. The model rejects the hypothesis of manifesting matter from extra dimensions. However, extra dimensions generate some attractive forces similar to gravity during the early evolution. Consequently, extra dimensions can be responsible for the past deceleration of the universe. The model seems to suggest an alternative mechanism pointing to a smooth transition from a decelerated phase to accelerated phase where the extra dimensions cause the transition. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
172 KiB  
Abstract
Dark Matter, Dark Energy and Something Else in 5D Theory
by Boris G. Aliyev
Phys. Sci. Forum 2021, 2(1), 7; https://doi.org/10.3390/ECU2021-09278 - 22 Feb 2021
Viewed by 1177
Abstract
It is shown, that (4+1)—and (3+1+1)—reductions of the geodetic equations in 5D theory with scalar field φ=G55 and out of the 5D optics inevitably lead to the [...] Read more.
It is shown, that (4+1)—and (3+1+1)—reductions of the geodetic equations in 5D theory with scalar field φ=G55 and out of the 5D optics inevitably lead to the new concept of the Lorentz-type relativistic mass m^0 of the 5D test particle. Due to the imposition of the x5—cylindricity condition, one can obtain an integral of the 5D particle’s motion along x5; it gives its electric charge. Thus, one can obtain an exact expression for m^0. In this expression m^0 depends on the field φ through an electric charge, so there is not probably any need for a scalar charge in Nature at all. Furthermore, one can compactly express the m^0 through the mass angle χn and additionally hypothesize about the possible complex structure of m^0. It soundly leads one to the deeper understanding of the quantum properties of the matter. All of these conceptions also turn one to the idea that this mass m^0 may contribute to the recently discovered in the Universe dark matter and dark energy and also be one of the possible reasons for the Universe’s expansion. The next suggestive result in the 5D theory is connected with the (4+1)—reduction of the 5D Ricci identities. It leads one to certain connections between the 4D physicogeometrical values and permits one to obtain the first pair of Maxwell equations with the non-zero soliton-type r.h.s. and establishes the connection with the second pair of them. It subsequently leads one to the idea about the magnetic monopole’s existence in the early Universe. It is shown, that this non-zero r.h.s. vanishes together with the imposition of the x5—cylindricity condition. The peculiarity of this process permits one to hypothesize soundly about the existence of the topological second-order transition in the Universe, which leads one to the superfluid state and possibly accelerates its expansion. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
160 KiB  
Abstract
T and C Symmetry Breaking in Algebraic Quantum Field Theory
by Vadim Monakhov
Phys. Sci. Forum 2021, 2(1), 15; https://doi.org/10.3390/ECU2021-09285 - 22 Feb 2021
Viewed by 1138
Abstract
We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra). The proposed approach is based on the use of Grassmann densities in the momentum space and their derivatives with respect to the construction from [...] Read more.
We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra). The proposed approach is based on the use of Grassmann densities in the momentum space and their derivatives with respect to the construction from these densities of both basis Clifford vectors of spacetime and the spinor vacuum. We have shown the existence of two vacua: normal and alternative. We have proven that CPT is the real structure operator in the theory of Krein spaces. C and T operators transform a normal vacuum into an alternative one, which leads to the breaking of these symmetries. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
163 KiB  
Abstract
Particle Hunters. Special Relativity as a Tool for Discovery in Particle Physics
by Lorenzo Galante
Phys. Sci. Forum 2021, 2(1), 18; https://doi.org/10.3390/ECU2021-09325 - 22 Feb 2021
Viewed by 1286
Abstract
Special relativity is a fundamental tool for the analysis of collision events in particle physics. This provides the opportunity to create educational environments in which interactions between theory and experimental data occur, an opportunity whose potentiality is worth exploring. An interactive application to [...] Read more.
Special relativity is a fundamental tool for the analysis of collision events in particle physics. This provides the opportunity to create educational environments in which interactions between theory and experimental data occur, an opportunity whose potentiality is worth exploring. An interactive application to analyze a collision between particles is presented as a tool that opens a mystery students must solve using special relativity as an inquiry tool. As in a Role Play Game, students are introduced into an environment they have to empathise with. They are asked to play the role of a particle physicist, to analyze a collision between a pion and a helium nucleus and to solve the mystery that arises from their analysis: momentum seems not to be conserved! Will they have to dismiss the conservation law or start the hunt for an undetected particle responsible for the missing momentum? As in many Role Play Games, the participants have special powers or attitudes. Here, the special power comes from Einstein’s energy–momentum–mass relation, which will be the magic wand leading students toward the solution of the puzzle. “Particle Hunters” is an educational environment designed to promote a deeper understanding of specific aspects of special relativity and to foster empathy and critical thinking throughout the learning process. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
161 KiB  
Abstract
On Filaments, Prolate Halos and Rotation Curves
by Kirill Zatrimaylov
Phys. Sci. Forum 2021, 2(1), 19; https://doi.org/10.3390/ECU2021-09298 - 22 Feb 2021
Viewed by 1024
Abstract
We propose a simple geometrical mechanism for the flattening of galactic rotation curves at large distances, the local compression of field lines around their planes induced either by the presence of thin string-like objects at the centers of galaxies or by elongated dark [...] Read more.
We propose a simple geometrical mechanism for the flattening of galactic rotation curves at large distances, the local compression of field lines around their planes induced either by the presence of thin string-like objects at the centers of galaxies or by elongated dark mater halos, and elaborate on its possible role in nature. We fit 83 rotation curves from the SPARC database with logarithmic potentials produced by a thin “wire” at the origin and then, after selecting 2 galaxies that yield the most interesting fits, analyze them with an alternative model, deformed versions of two popular models of dark-matter halos. Our conclusion is that the presence of a filament clearly improves the fit quality in a number of cases, while bulged dark matter profiles have a lesser effect. If taken at face value, these results would imply the presence of elongated mass distributions away from the galactic plane in a number of galaxies, and may also have some indirect impact on the controversy between cold dark matter (CDM), self-interacting dark matter (SiDM), and modified Newtonian dynamics (MOND). Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
162 KiB  
Abstract
Immersing the Schwarzschild Black Hole in Test Nonlinear Electromagnetic Fields
by Ana Bokulić and Ivica Smolić
Phys. Sci. Forum 2021, 2(1), 22; https://doi.org/10.3390/ECU2021-09301 - 22 Feb 2021
Viewed by 1124
Abstract
Killing vector fields can be used as gauge vector potentials since the associated electromagnetic field tensor automatically satisfies the source-free Maxwell’s equations in vacuum spacetimes. This fact enabled Wald to find the form of the electromagnetic tensor corresponding to the Kerr black hole [...] Read more.
Killing vector fields can be used as gauge vector potentials since the associated electromagnetic field tensor automatically satisfies the source-free Maxwell’s equations in vacuum spacetimes. This fact enabled Wald to find the form of the electromagnetic tensor corresponding to the Kerr black hole immersed in a uniform test magnetic field. We present the generalisation of this result, which is valid for static black holes surrounded by nonlinear electromagnetic fields. The first obstacle we encountered when dealing with the nonlinear electrodynamics was that the above-described ansatz no longer works. Secondly, finding the exact solution in a closed form proved to be a rather challenging task because it would require solving a highly nonlinear differential equation. The alternative approach is via perturbative expansion around the original Wald’s solution. We obtain the equation which determines the lowest order correction to the gauge vector field 1-form and magnetic scalar potential. With the main focus on the Born–Infeld and Euler–Heisenberg theories on the Schwarzschild background, we calculate the aforementioned correction. Additionally, we show that this perturbative correction does not change electric and magnetic Komar charges or the asymptotic behaviour of the field. Finally, stating physical arguments, we justify the usage of the perturbative approach. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
153 KiB  
Abstract
Lambda Perturbations and Instability of Keplerian Orbits in the Expanding Universe
by Yurii Dumin
Phys. Sci. Forum 2021, 2(1), 23; https://doi.org/10.3390/ECU2021-09296 - 22 Feb 2021
Viewed by 1100
Abstract
Since the concept of Dark Energy (i.e., effective Lambda-term in the GR equations) became a commonly accepted paradigm in cosmology, numerous authors have analyzed its effects on the dynamics of celestial bodies. However, such calculations were usually only carried out in the framework [...] Read more.
Since the concept of Dark Energy (i.e., effective Lambda-term in the GR equations) became a commonly accepted paradigm in cosmology, numerous authors have analyzed its effects on the dynamics of celestial bodies. However, such calculations were usually only carried out in the framework of the static Schwarzschild–deSitter metric, which does not possess the adequate cosmological asymptotics at infinity and, as a result, only the conservative perturbations of the orbits have been taken into account. The aim of the present work therefore is to use the more realistic Robertson–Walker asymptotics and thereby also analyze the nonconservative (secular) perturbations of Keplerian orbits. As a mathematical tool, we employ the modified Kottler metric, which was derived in our earlier paper. As follows from our analysis of the motion of a test body in the field of a gravitating mass, the resulting perturbations of the Keplerian orbits depend on a complex interplay between three crucial parameters of the problem—the initial radius of the orbit, Schwarzschild and deSitter radii—which differ from each other by many orders of magnitude. Namely, if Lambda-term is sufficiently small (i.e., the deSitter radius is large), then orbital perturbation is almost completely compensated by the gravitational attraction. Next, when the magnitude of Lambda increases, the corresponding secular perturbation becomes significant and can reach the rate of the standard Hubble flow. This fact may have important consequences for the long-term dynamics of planets and stellar binaries. At last, if the Lambda-term increases further, the perturbation becomes so strong that the original orbit is completely destroyed and the test body escapes to infinity (i.e., a kind of “sling effect” takes place). This might be relevant, e.g., to the formation of the so-called “hypervelocity stars”. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
167 KiB  
Abstract
Quantum Physics Literacy Aimed at K12 and General Public
by Caterina Foti, Daria Anttila, Sabrina Maniscalco and Marilù Chiofalo
Phys. Sci. Forum 2021, 2(1), 36; https://doi.org/10.3390/ECU2021-09322 - 22 Feb 2021
Cited by 1 | Viewed by 1298
Abstract
Teaching quantum physics to K12 students and the general public represents an inevitable must, while quantum technologies revolutionize our lives. Quantum literacy is a formidable challenge and an extraordinary opportunity for a massive cultural uplift, where citizens learn how to engender creativity and [...] Read more.
Teaching quantum physics to K12 students and the general public represents an inevitable must, while quantum technologies revolutionize our lives. Quantum literacy is a formidable challenge and an extraordinary opportunity for a massive cultural uplift, where citizens learn how to engender creativity and practice a new way of thinking, essential for smart community building. Scientific thinking hinges on analyzing facts and creating understanding, then formulating these with dense mathematical language for later fact checking. Within classical physics, learners’ intuition can be educated via classroom demonstrations of everyday life phenomena. Their understanding can even be framed with the mathematics suited to their instruction degree. For quantum physics instead, we have no experience of quantum phenomena, and the required mathematics is beyond non-expert reach. Therefore, educating intuition needs imagination. Without resorting to experiments and some degree of formal framing, educators face the risk of providing only evanescent tales, often misled, while resorting to familiar analogies. Here, we report on the realization of QPlayLearn, an online platform conceived to explicitly address challenges and opportunities of massive quantum literacy. QPlayLearn’s mission is to provide multilevel education on quantum science and technologies to anyone, regardless of age and background. To this aim, innovative interactive tools enhance the learning process effectiveness, fun, and accessibility, while remaining grounded in scientific correctness. Examples are games for basic quantum physics teaching, on-purpose designed animations, and easy-to-understand explanations on terminology and concepts by global experts. As a strategy for massive cultural change, QPlayLearn offers diversified content for different target groups, from primary school all the way to university physics students. It is also addressed to companies wishing to understand the potential of the emergent quantum industry, journalists, and policy makers who need to quickly to understand what quantum technologies are about, and all quantum science enthusiasts. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
153 KiB  
Abstract
The Cosmological Model Based on the Uncertainty-Mediated Dark Energy
by Yurii Dumin
Phys. Sci. Forum 2021, 2(1), 37; https://doi.org/10.3390/ECU2021-09515 - 19 Mar 2021
Viewed by 1329
Abstract
The existence of the effective Lambda-term is a commonly accepted paradigm of modern cosmology, but the physical essence of this quantity remains absolutely unknown, and its numerical values are drastically different in the early and modern universe. In fact, the Lambda-term is usually [...] Read more.
The existence of the effective Lambda-term is a commonly accepted paradigm of modern cosmology, but the physical essence of this quantity remains absolutely unknown, and its numerical values are drastically different in the early and modern universe. In fact, the Lambda-term is usually introduced in the literature either by postulating arbitrary additional terms in the Lagrangians or by employing the empirical equations of state. In our recent series of papers (Yu.V. Dumin. Grav. and Cosmol., v.25, p.169 (2019); v.26, p. 259 (2020); v.27, in press (2021)), we tried to provide a more rigorous physical basis for the effective Lambda-term, starting from the time-energy uncertainty relation in the Mandelstam–Tamm form, which is appropriate for the long-term evolution of quantum systems. This results in the time-dependent Lambda-term, decaying as 1/t. The uncertainty-mediated cosmological model possesses a number of specific features, some of which look rather appealing: (1) While the standard cosmology involves a few very different stages (governed by the Lambda-term, radiation, dustlike matter, and again the Lambda-term), our model provides a universal description of the entire evolution of the universe by the same “quasi-exponential” function. (2) As follows from the analysis of causal structure, the present-day cosmological horizon comprises a single domain developing from the Bing Bang. Therefore, the problems of the homogeneity and isotropy of matter, the absence of topological defects, etc. should be naturally resolved. (3) Besides, our model naturally explains the observed approximately flat 3D space, i.e., the solution with zero curvature is formed “dynamically”, starting from the arbitrary initial conditions. (4) The age of the universe turns out to be much greater than in the standard cosmology; but this should not be a crucial drawback, because the most of problems are associated with insufficient rather than excessive age of the universe. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
163 KiB  
Abstract
Dynamics of Anisotropic Cylindrical Collapse in Energy-Momentum Squared Gravity
by Muhammad Sharif and Muhammad Zeeshan Gul
Phys. Sci. Forum 2021, 2(1), 40; https://doi.org/10.3390/ECU2021-09513 - 19 Mar 2021
Viewed by 1451
Abstract
This paper deals with the dynamics of cylindrical collapse with anisotropic matter configuration in the context of energy-momentum squared gravity. This covariant generalization of general relativity allows the presence of T_abT^ab in the action of functional theory. Consequently, the relevant field equations are [...] Read more.
This paper deals with the dynamics of cylindrical collapse with anisotropic matter configuration in the context of energy-momentum squared gravity. This covariant generalization of general relativity allows the presence of T_abT^ab in the action of functional theory. Consequently, the relevant field equations are different from general relativity only in the presence of matter sources. In this theory, there is a maximum energy density and a minimum scale factor of the early universe. This means that there is a bounce at early times which avoids the presence of an early-time singularity. Moreover, this theory possesses a true sequence of cosmological eras. However, the cosmological constant does not play an important role in the early times and becomes important only after the matter-dominated era. In this theory, the “repulsive” nature of the cosmological constant plays a crucial role at early times in resolving the singularity. We formulate the corresponding field equations as well as junction conditions. We construct dynamical equations through the Misner–Sharp technique and examine the impact of energy-momentum squared gravity on the collapse rate. We develop a relation among fluid parameters, correction terms and Weyl scalar and examine the effects of anisotropy, effective matter variables and correction terms on the collapsing phenomenon. Due to the presence of anisotropic pressure, spacetime is no longer considered to be conformally flat. To obtain conformally flat spacetime, we neglect the impact of anisotropy and assume the isotropic matter distribution which yields homogeneity of the energy density and conformally flat spacetime. The hydrodynamical force determines the stability of the system and prevents the collapsing as well as expanding process for the constant energy-momentum squared gravity model. We conclude that positive correction terms and anisotropy provide the anti-gravitational behavior leading to the stability of self-gravitating objects and hence prevent the collapsing process. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
171 KiB  
Abstract
Compact Objects in Brans-Dicke Gravity
by Muhammad Sharif and Amal Majid
Phys. Sci. Forum 2021, 2(1), 42; https://doi.org/10.3390/ECU2021-09276 - 22 Feb 2021
Viewed by 1104
Abstract
This paper aims to investigate the existence and properties of anisotropic quark stars in the context of the self-interacting Brans–Dicke theory. In this theory, the gravitational constant in general relativity is replaced by a dynamical massive scalar field accompanied by a potential function. [...] Read more.
This paper aims to investigate the existence and properties of anisotropic quark stars in the context of the self-interacting Brans–Dicke theory. In this theory, the gravitational constant in general relativity is replaced by a dynamical massive scalar field accompanied by a potential function. Researchers believe that strange stars may evolve from neutron stars when neutrons fail to endure the extreme temperature and pressure in the interior region. As a consequence, they breakdown into their constituent particles, known as quarks. In order to construct a well-behaved quark star model under the influence of a massive scalar field, we formulate the field equations by employing the MIT bag model. The MIT bag model (strange quark matter equation of state) is the most suitable choice for quark stars as it has successfully described the compactness of certain stellar bodies. Furthermore, the estimates of mass of quark stars based on the data from the cosmic events GW170817 and GW190425 support the choice of MIT bag model. The model is developed by considering three types of quark matter: strange, up, and down. The bag constant involved in the model differentiates between false and true vacuum. We consider a static sphere with anisotropic fluid and employ the observed masses and radii of the strange star candidates (RXJ 1856-37 and PSR J1614-2230) in the matching conditions at the boundary to evaluate the value of the bag constant. Further, we evaluate the impact of the massive scalar field on state parameters and investigate the viability (via energy conditions) as well as stability (through the speed of sound constraints) of the self-gravitating objects. It is found that the obtained values of the bag constant lie within the accepted range (58.9 MeV/fm3B ≤ 91.5 MeV/fm3). Moreover, the anisotropic structure meets the necessary viability and stability criteria. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
1 pages, 173 KiB  
Abstract
Nonperturbative QED on the Hopf Bundle
by Vladimir Dzhunushaliev and Vladimir Folomeev
Phys. Sci. Forum 2021, 2(1), 43; https://doi.org/10.3390/ECU2021-09286 - 22 Jul 2021
Viewed by 1952
Abstract
We consider the Dirac equation and Maxwell’s electrodynamics in ×S3 spacetime, where a three-dimensional sphere is the Hopf bundle S3S2. The method of nonperturbative quantization of interacting Dirac and Maxwell fields is suggested. The corresponding [...] Read more.
We consider the Dirac equation and Maxwell’s electrodynamics in ×S3 spacetime, where a three-dimensional sphere is the Hopf bundle S3S2. The method of nonperturbative quantization of interacting Dirac and Maxwell fields is suggested. The corresponding operator equations and the infinite set of the Schwinger–Dyson equations for Green’s functions is written down. To illustrate the suggested scheme of nonperturbative quantization, we write a simplified set of equations describing some physical situation. Additionally, we discuss the properties of quantum states and operators of interacting fields. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
168 KiB  
Abstract
Monopole Solutions in SU(2) Yang–Mills and Nonlinear Spinor Field Theory
by Serikbolova Albina Askarovna and Dzhunushaliev Vladimir Dzhumakadyrovich
Phys. Sci. Forum 2021, 2(1), 47; https://doi.org/10.3390/ECU2021-09287 - 22 Feb 2021
Viewed by 1106
Abstract
Monopole solutions in SU(2) Yang–Mills theory, which interact with massive nonlinear spinor fields, described by the nonlinear Dirac equation, are obtained. These solutions describe a magnetic monopole created by a spherical lump of nonlinear spinor fields. It is shown that the monopole solutions [...] Read more.
Monopole solutions in SU(2) Yang–Mills theory, which interact with massive nonlinear spinor fields, described by the nonlinear Dirac equation, are obtained. These solutions describe a magnetic monopole created by a spherical lump of nonlinear spinor fields. It is shown that the monopole solutions obtained differ in principle from the ‘t Hooft–Polyakov monopole so that (a) it is topologically trivial; (b) the radial magnetic field decreases as r3; (c) the Higgs field is not necessary for its existence. It is demonstrated that the energy spectrum of such a system possesses a global minimum, the appearance of which is due exclusively to the nonlinearity of the Dirac spinor fields. This global minimum can be considered a mass gap, i.e., the energy difference between a vacuum and the next lowest energy state. A similar minimum was found for the energy spectrum of regular solutions to the nonlinear Dirac equation and this minimum is called “the lightest stable particle”. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
161 KiB  
Abstract
Scientific Concepts within Reach of Young Learners: Support from the Educational Research Literature
by David F. Treagust
Phys. Sci. Forum 2021, 2(1), 58; https://doi.org/10.3390/ECU2021-09317 - 22 Feb 2021
Viewed by 1166
Abstract
For four or five decades, science educators, including physics educators, have benefited from the work of Piaget and neo-Piagetians. Piaget’s theory of cognitive development argues that children move through four different stages of mental development, how they acquire knowledge and the role of [...] Read more.
For four or five decades, science educators, including physics educators, have benefited from the work of Piaget and neo-Piagetians. Piaget’s theory of cognitive development argues that children move through four different stages of mental development, how they acquire knowledge and the role of active learning. Among other issues, neo-Piagetians considered that working memory capacity is affected by biological maturation, restricting young children’s ability to acquire complex thinking and reasoning skills. I want to emphasise that these educational developments largely benefitted science teachers and young science learners with many new and improved science curricula and teaching methods. However, challenges to these views arose when educational researchers observed children’s learning that did not neatly fit these cognitive stages or restrictions. Since the mid 1990’s, there has been a growing body of research demonstrating that, with appropriate scaffolding by teachers and opportunities for student collaboration, young learners can engage with and understand abstract scientific concepts that might otherwise be seen to be out of reach for this age group. Based on this premise from recent research in educational psychology, the work of the Einstein-First group has embarked on studies that demonstrate how young learners from primary school onwards can engage and learn abstract Einsteinian physics concepts that were previously considered best taught only in upper high school. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
151 KiB  
Abstract
Developing a Cosmology Unit for Year 10 Students to Determine Hubble’s Constant Using Gravitational Waves
by Darren McGoran
Phys. Sci. Forum 2021, 2(1), 60; https://doi.org/10.3390/ECU2021-09316 - 22 Feb 2021
Viewed by 1081
Abstract
Modern science curricula contain the foundations and scaffolding to allow the syllabus to include modern physics concepts that are not normally taught. The Big Bang can be refined to include how gravitational waves are being used to determine Hubble’s Constant. Students will develop [...] Read more.
Modern science curricula contain the foundations and scaffolding to allow the syllabus to include modern physics concepts that are not normally taught. The Big Bang can be refined to include how gravitational waves are being used to determine Hubble’s Constant. Students will develop background knowledge about concepts such as expansion of spacetime, particle-antiparticle production in the early universe, emission/absorption spectra, and redshift which will enable them to appreciate the meaning and significance of Hubble’s Constant. The work of Slipher, Lemaitre, and Hubble provide a case study for Science as a Human Endeavour. Science Inquiry Skills are included through activities on redshift, parsecs, and the Hubble Constant. The content of the unit is presented using practical activities, models, worksheets, videos, power points, and consolidation questions. Student and teacher feedback will be used to gauge the effectiveness of the unit; including the ability of the students to grasp the concepts, the students’ level of enjoyment, and the teacher’s feelings on facilitating the unit. In this presentation, I will introduce an approach to cosmology in which students learn about the Hubble Constant, and how gravitational waves allow its measurement without reference to the complex and messy cosmic distances ladder. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)

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611 KiB  
Proceeding Paper
Dark Atom Solution for the Puzzles of Direct Dark Matter Search
by Timur Bikbaev, Maxim Khlopov and Andrey Mayorov
Phys. Sci. Forum 2021, 2(1), 3; https://doi.org/10.3390/ECU2021-09263 - 22 Feb 2021
Viewed by 1481
Abstract
The puzzle of direct dark matter searches can b solved in the model of an OHe dark atom, which consists of a stable O lepton core and a nuclear interacting (alpha particle) shell of a primordial helium nuclei. In this [...] Read more.
The puzzle of direct dark matter searches can b solved in the model of an OHe dark atom, which consists of a stable O lepton core and a nuclear interacting (alpha particle) shell of a primordial helium nuclei. In this model, positive results of the DAMA group can be explained by annual modulation of radiative capture of OHe atoms to low-energy bound states with sodium nuclei, which does not take place under the conditions of other underground experiments. The existence of such a low-energy bound state is the key problem of the OHe model of composite dark matter. The complexity of this problem, which has not found a correct solution during the last 15 years, requires a consistent approach to its solution. Within the framework of the proposed approach to such modeling, in order to reveal the essence of the processes of interaction of OHe with the nuclei of baryonic matter, a classical model is used, to which the effects of quantum physics and final size of nuclei are successively added. The numerical model of the interaction of the “dark” OHe atom with the nuclei is developed by successive addition of realistic features of a quantum-mechanical description to the initial classical problem of three point-like bodies (O particle, the He nucleus and the target nucleus). The developed approach leads to a numerical model describing the OHe-nucleus system with self-consistent accounting for nuclear attraction and electromagnetic interaction of dark atom with nuclei. The model can prove the interpretation of the results of the direct underground experimental dark matter search in the terms of the dark atom hypothesis. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>The density of the distribution of the coordinates of the <math display="inline"><semantics> <mi>α</mi> </semantics></math>-particle in the orbit corresponding to the ground state of the system.</p>
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<p>Coordinate system <span class="html-italic">O</span>He—nucleus.</p>
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<p><math display="inline"><semantics> <mi>α</mi> </semantics></math>-particle and particle <math display="inline"><semantics> <msup> <mi>O</mi> <mrow> <mo>−</mo> <mo>−</mo> </mrow> </msup> </semantics></math> trajectories.</p>
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<p>The trajectory of <math display="inline"><semantics> <mi>α</mi> </semantics></math>-particle and the <math display="inline"><semantics> <msup> <mi>O</mi> <mrow> <mo>−</mo> <mo>−</mo> </mrow> </msup> </semantics></math> in the XY plane.</p>
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2919 KiB  
Proceeding Paper
Particle Physics at Primary Schools: A Report on the Italian Project
by Sandra Malvezzi and Andrea Quadri
Phys. Sci. Forum 2021, 2(1), 5; https://doi.org/10.3390/ECU2021-09284 - 22 Feb 2021
Cited by 1 | Viewed by 1426
Abstract
We report on an ongoing project aimed to teach particle physics in primary schools. The project is based on the original format by C. Lazzeroni and M. Pavlidou at the University of Birmingham, UK. The Italian version of the project emphasizes the following [...] Read more.
We report on an ongoing project aimed to teach particle physics in primary schools. The project is based on the original format by C. Lazzeroni and M. Pavlidou at the University of Birmingham, UK. The Italian version of the project emphasizes the following aspects: (1) the relevance of the teachers’ training in order to make the project sustainable on a large scale and for a long period of time, overcoming the risk of occasional interest arousal about Particle Physics; (2) importance of an integrated approach where the Particle Physics workshops are put into the context of the regular learning school activities as well as outreach activities for parents. The program has run in six primary schools in Northern Italy since 2017, and it has evolved into a structured training program for teachers in collaboration with INFN in 2019. From the experience gathered in these years, the main benefits of the project include increased motivation, improved attitude towards science, and reduced gender bias in science-related activities. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Distribution of local Lyapunov exponents for a (<b>a</b>) regular orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>1.96</mn> <mo>,</mo> <mn>4.91</mn> <mo>)</mo> </mrow> </semantics></math> and (<b>b</b>) chaotic orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.39</mn> <mo>,</mo> <mn>2.85</mn> <mo>)</mo> </mrow> </semantics></math> in the standard map with <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>.</p>
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<p>Rate of convergence of the block bias due to finite number of mapping iterations for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math> with a regular orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>1.96</mn> <mo>,</mo> <mn>4.91</mn> <mo>)</mo> </mrow> </semantics></math> (diamond) and a chaotic orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.39</mn> <mo>,</mo> <mn>2.85</mn> <mo>)</mo> </mrow> </semantics></math> (x) and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> with a regular orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>1.76</mn> <mo>,</mo> <mn>0.33</mn> <mo>)</mo> </mrow> </semantics></math> (diamond), a confined chaotic orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.02</mn> <mo>,</mo> <mn>2.54</mn> <mo>)</mo> </mrow> </semantics></math> (circle) and a chaotic orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.2</mn> <mo>,</mo> <mn>5.6</mn> <mo>)</mo> </mrow> </semantics></math> (x). The graphs show <math display="inline"><semantics> <msub> <mover accent="true"> <mi>λ</mi> <mo>˜</mo> </mover> <mi>T</mi> </msub> </semantics></math>, the median of <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>T</mi> </msub> </semantics></math> for each <span class="html-italic">T</span>, with <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>λ</mi> <mo>˜</mo> </mover> <mi>T</mi> </msub> <mo>=</mo> <mi>λ</mi> <mo>+</mo> <mi>c</mi> <mo>/</mo> <mi>T</mi> </mrow> </semantics></math> fitted by linear regression of <math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mover accent="true"> <mi>λ</mi> <mo>˜</mo> </mover> <mi>T</mi> </msub> </mrow> </semantics></math> on <span class="html-italic">T</span>. The gray areas correspond to the standard deviation for 1000 test points.</p>
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<p>Local Lyapunov exponents in phase space of the standard map calculated with <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> mapping iterations for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>.</p>
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<p>Orbit classification in standard map, (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>. The color map indicates the probability that the orbit is regular.</p>
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<p>Percentage of misclassified orbits using a Bayesian classifier trained with 200 orbits for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. 100 test orbits on an equally spaced grid in the range of <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mi>π</mi> <mo>]</mo> <mo>×</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo>]</mo> </mrow> </semantics></math> are classified as regular or chaotic depending on their LLE.</p>
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<p>Total Sobol’ indices as a function of time for three orbits of the standard map with <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>—upper: chaotic orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>0.2</mn> <mo>,</mo> <mn>5.6</mn> <mo>)</mo> </mrow> </semantics></math>, middle: regular orbit <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mn>1.76</mn> <mo>,</mo> <mn>0.33</mn> <mo>)</mo> </mrow> </semantics></math>, lower: regular orbit very close to fixed point <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>p</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <mi>π</mi> <mo>,</mo> <mn>0.1</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Total Sobol’ indices (Equation (<a href="#FD15-psf-02-00005" class="html-disp-formula">15</a>)) for the standard map with <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> averaged from <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>30</mn> </mrow> </semantics></math>.</p>
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4387 KiB  
Proceeding Paper
Teaching the Equivalence Principle through a Combination of Real-Life Experiments and Computer Simulations
by Efstratios Kapotis and Panagiotis Tsakonas
Phys. Sci. Forum 2021, 2(1), 6; https://doi.org/10.3390/ECU2021-09281 - 22 Feb 2021
Viewed by 1453
Abstract
The need to transform scientific knowledge to materials suitable for teaching school students is a constant challenge for the educational community. Although it has been more than a century since quantum mechanics and the theory of relativity were established, both topics continue to [...] Read more.
The need to transform scientific knowledge to materials suitable for teaching school students is a constant challenge for the educational community. Although it has been more than a century since quantum mechanics and the theory of relativity were established, both topics continue to be treated as modern physics, and only recently did they begin to be taught to students of levels prior to higher education. The work at hand is part of a larger effort to introduce the general theory of relativity in schools. To this end, we have devised appropriate experiments and computer simulation software. In particular, we present an educational simulation software that we created for the teaching of the Equivalence Principle. The implementation was applied to 120 undergraduate students of the Pedagogical Department of the University of Athens who do not major in physics but will be expected to teach young students the basic principles of relativity. The simulation software enables the user to measure forces inside a gravitational field and compare them to those exerted on bodies being accelerated. The controls incorporated in the software aim to motivate students to perform a variety of experiments, investigating every possible combination of parameters, in the hope to help them overcome most of the learning difficulties highlighted by previous research. The encouraging results of the research confirm the need to continue to fill gaps in the fragmented instruction of physics in schools. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Improvised elevator for conducting experiments concerning the EP: (<b>a</b>) materials needed to assemble the device; (<b>b</b>) elevator in free fall; (<b>c</b>) elevator moving upwards at constant acceleration; (<b>d</b>) spring scale measurement during free fall equaling 0 N, 0 g, while a 100 g body is suspended from the spring’s free endpoint.</p>
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<p>Indicative software snapshots showing a number of ways of elevator movement (various values of velocity and acceleration, as well as direction of movement), while measuring magnitudes of mass, weight, normal force and showing corresponding vectors.</p>
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<p>Sample steps of (<b>a</b>) Experimentation and Generalization—Consolidation of knowledge from the digital worksheet showing weightlessness in free fall flight, designs for future space stations recreating gravity through acceleration and (<b>b</b>) instructions on constructing an improvised “Einstein elevator—box”. The rest of the steps are accessible via the left side buttons.</p>
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<p>Three of the multiple-choice questions from the evaluation questionnaire of the intervention: (<b>a</b>) Questions 3 and 4, (<b>b</b>) Question 5.</p>
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274 KiB  
Proceeding Paper
Introducing Quantum Mechanics in High Schools: A Proposal Based on Heisenberg’s Umdeutung 
by Marco Di Mauro and Adele Naddeo
Phys. Sci. Forum 2021, 2(1), 8; https://doi.org/10.3390/ECU2021-09283 - 22 Feb 2021
Cited by 4 | Viewed by 2347
Abstract
Teaching and learning QM at high school as well as the undergraduate level is a highly non-trivial task. Indeed, major changes are required in understanding the new physical reality, and students have to deal with counterintuitive concepts such as uncertainty and entanglement as [...] Read more.
Teaching and learning QM at high school as well as the undergraduate level is a highly non-trivial task. Indeed, major changes are required in understanding the new physical reality, and students have to deal with counterintuitive concepts such as uncertainty and entanglement as well as advanced mathematical tools. In order to overcome these critical issues, a simple approach is presented here, which is based solely on two-vector and 2 × 2 matrix algebra. Furthermore, it could also enable educational institutions to fill the gap between high school curricula and the current scientific and technological advances in physics by allowing students to gain some insight into topics such as qubits and quantum computers. The inspiration behind our proposal as well as its firm theoretical foundation are based on the famous Umdeutung (reinterpretation) paper by W. Heisenberg, which introduces QM in matrix form. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
885 KiB  
Proceeding Paper
Electron Born Self-Energy Model for Dark Energy
by Bruce M. Law
Phys. Sci. Forum 2021, 2(1), 9; https://doi.org/10.3390/ECU2021-09300 - 22 Feb 2021
Viewed by 4490
Abstract
Dark Energy, a form of repulsive gravity, is causing an accelerated expansion of the Universe. Recent astrophysical measurements have confirmed this accelerated expansion where the ΛCDM model provides a quantitative description of this expansion rate. As is well known there are a number [...] Read more.
Dark Energy, a form of repulsive gravity, is causing an accelerated expansion of the Universe. Recent astrophysical measurements have confirmed this accelerated expansion where the ΛCDM model provides a quantitative description of this expansion rate. As is well known there are a number of free parameters of unknown origin in the ΛCDM model. In particular, the cosmological constant Λ (or Dark Energy (DE)) forms one of these free parameters. In this contribution we describe a recent model that attributes DE to the Born self-energy contained within the electric field which surrounds a finite-sized electron within the WHIM (Warm-Hot Intergalactic Medium). Upon using readily available literature values for the intergalactic (IG) baryon density, IG hydrogen ionization fraction, the best estimate for the electron radius, as well as, Hubble parameter data many properties associated with DE can be quantitatively explained. In particular, our model provides an explanation for (i) the magnitude of DE today, (ii) the DE to ordinary matter mass ratio today, (iii) has an equation of state of w = −1, as expected for DE, and (iv) exhibits a deceleration-acceleration transition at a redshift of z~0.8 in agreement with Hubble parameter observations. (v) Finally, the model provides a viable candidate for Dark Matter; the CDM in the ΛCDM model.Further details regarding this DE model can be found in Astrophys. Space Sci 2020, 365, 64. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Binned “WM456” Hubble parameter data <math display="inline"><semantics> <mrow> <mi>H</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> plotted as <math display="inline"><semantics> <mrow> <mi>H</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>/</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> versus <math display="inline"><semantics> <mi>z</mi> </semantics></math> (symbols). Various theoretical fits to this binned data (lines). Taken from [<a href="#B11-psf-02-00009" class="html-bibr">11</a>]. © AAS. Reproduced with permission.</p>
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<p>Fractional ionization <math display="inline"><semantics> <mrow> <msub> <mi>ν</mi> <mi>e</mi> </msub> </mrow> </semantics></math> plotted on a log-log graph as a function of redshift <math display="inline"><semantics> <mi>z</mi> </semantics></math> and time <math display="inline"><semantics> <mi>t</mi> </semantics></math>. Black inverted triangles: calculated using Equation (14); green squares: from computer simulations [<a href="#B7-psf-02-00009" class="html-bibr">7</a>]. Reprinted by permission from RightsLink: Springer Nature, Law, B. M., Astrophys Space Sci <b>365</b>, 64, [COPYRIGHT] (2020).</p>
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797 KiB  
Proceeding Paper
The Dark Universe Is Not Invisible
by Konstantin Zioutas, Vassilis Anastassopoulos, Athanasios Argiriou, Giovanni Cantatore, Serkant Ali Cetin, Antonios Gardikiotis, Dieter H. H. Hoffmann, Sebastian Hofmann, Marin Karuza, Abaz Kryemadhi, Marios Maroudas, Eric L. Matteson, Kaan Ozbozduman, Thomas Papaevangelou, Michael Perryman, Yannis K. Semertzidis, Ioannis Tsagris, Mary Tsagri, Georgios Tsiledakis, Dominik Utz and Edward L. Valachovicadd Show full author list remove Hide full author list
Phys. Sci. Forum 2021, 2(1), 10; https://doi.org/10.3390/ECU2021-09313 - 22 Feb 2021
Cited by 1 | Viewed by 2481
Abstract
Evidence of dark matter (DM) comes from long-range gravitational observations, where it is understood to not interact with ordinary matter. However, on a much smaller scale, a number of unexpected phenomena contradict this idea of DM. This is because some solar activity and [...] Read more.
Evidence of dark matter (DM) comes from long-range gravitational observations, where it is understood to not interact with ordinary matter. However, on a much smaller scale, a number of unexpected phenomena contradict this idea of DM. This is because some solar activity and the dynamic Earth atmosphere might arise from DM streams. Gravitational (self-)focusing effects by the Sun or its planets of streaming DM fit as the underlying process, e.g., for the otherwise puzzling 11-year solar cycle, the mysterious heating of the solar corona with its fast temperature inversion, etc. Observationally driven, we arrive to suggest an external impact by as yet overlooked “streaming invisible matter”, which reconciles some of the investigated mysterious observations. Unexpected planetary relationships exist for the dynamic Sun and Earth atmosphere and are considered as the signature for streaming DM. Then, focusing of DM streams could also occur in exoplanetary systems, suggesting for the first time the carrying out of investigations by searching for the associated stellar activity as a function of the exoplanetary orbital phases. The entire observationally driven reasoning is suggestive for highly cross-disciplinary approaches that also include (puzzling) biomedical phenomena. Favoured candidates from the dark sector are the highly ionizing anti-quark nuggets, magnetic monopoles and also particles such as dark photons. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>(<b>a</b>) The dependence of the coronal elemental composition [<a href="#B19-psf-02-00010" class="html-bibr">19</a>] to the photospheric one (A<sub>c</sub>/A<sub>p</sub>), given here by FIP / BIN, is projected on heliocentric longitudes for Earth (left) and the combined Mercury—Venus dependence (right). The relative min⇔ max amplitude is 14% and 18%, respectively; (<b>b</b>) the dependence of the relative Nr. of magnetic bright points (MBPs) [<a href="#B20-psf-02-00010" class="html-bibr">20</a>] projected on heliocentric longitudes of Venus (left) and Earth (right). The estimated error per BIN is about 3.5%. This also follows from the rather smooth shape of Earth’s spectral shape (right). The relative min⇔ max amplitude is 10% and 14%. See also <a href="#app1-psf-02-00010" class="html-app">Supplementary Materials</a> with more relevant information.</p>
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<p>Schematic representation of gravitational (self-)focusing effects of DM streams by the Sun, Earth, Venus, Mercury and/or Moon: (Top) gravitational focusing effect by the solar system. In this configuration, the galactic center is on the right side and in the opposite direction of the incident DM stream; (Bottom) the self-focusing effect of incident low speed streams reflects the dominating free fall towards the Sun; the flux enhancement increases with (<span class="html-italic">v</span><sub>incident</sub>/<span class="html-italic">v</span><sub>escape</sub>)<sup>2</sup>. The flux towards Earth can also be gravitationally modulated by the intervening Moon [<a href="#B10-psf-02-00010" class="html-bibr">10</a>]. See also <a href="#app1-psf-02-00010" class="html-app">Supplementary Materials</a> for additional information related to these scetches.</p>
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214 KiB  
Proceeding Paper
An Overview of Black Hole Chemistry
by Jamil Ahmed
Phys. Sci. Forum 2021, 2(1), 11; https://doi.org/10.3390/ECU2021-09308 - 22 Feb 2021
Viewed by 2437
Abstract
The understanding the thermodynamic behavior of black holes using the concepts of chemistry will be discussed here. To establish the complete correspondence between the thermodynamics of an ordinary system and the thermodynamics of black holes, recent proposals suggest the identification of the mass [...] Read more.
The understanding the thermodynamic behavior of black holes using the concepts of chemistry will be discussed here. To establish the complete correspondence between the thermodynamics of an ordinary system and the thermodynamics of black holes, recent proposals suggest the identification of the mass of a black hole as the chemical enthalpy of an ordinary thermodynamic system. Similarly, the negative cosmological constant, surface gravity, and horizon area of a black hole is identified as the pressure, temperature, and entropy of a thermodynamic system. Consequently, black holes behave analogously to a variety of everyday phenomena. This allows an understanding of black holes using concepts of chemistry such as Van der Waals fluids, phase transitions, etc. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
576 KiB  
Proceeding Paper
Timescales for Detecting Magnetized White Dwarfs in Gravitational Wave Astronomy
by Surajit Kalita
Phys. Sci. Forum 2021, 2(1), 12; https://doi.org/10.3390/ECU2021-09310 - 22 Feb 2021
Viewed by 1461
Abstract
Over the past couple of decades, researchers have predicted more than a dozen super-Chandrasekhar white dwarfs from the detections of over-luminous type Ia supernovae. It turns out that magnetic fields and rotation can explain such massive white dwarfs. If these rotating magnetized white [...] Read more.
Over the past couple of decades, researchers have predicted more than a dozen super-Chandrasekhar white dwarfs from the detections of over-luminous type Ia supernovae. It turns out that magnetic fields and rotation can explain such massive white dwarfs. If these rotating magnetized white dwarfs follow specific conditions, they can efficiently emit continuous gravitational waves and various futuristic detectors, viz. LISA, BBO, DECIGO, and ALIA can detect such gravitational waves with a significant signal-to-noise ratio. Moreover, we discuss various timescales over which these white dwarfs can emit dipole and quadrupole radiations and show that in the future, the gravitational wave detectors can directly detect the super-Chandrasekhar white dwarfs depending on the magnetic field geometry and its strength. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>A cartoon diagram of a magnetized rotating WD pulsar. Here <math display="inline"><semantics> <msup> <mi>z</mi> <mo>′</mo> </msup> </semantics></math> and <span class="html-italic">z</span> are, respectively, the rotation and magnetic field axes.</p>
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<p>Density isocontours of magnetized WDs with central density <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>c</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mn>10</mn> </msup> </mrow> </semantics></math> g cm<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math>.</p>
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<p><math display="inline"><semantics> <msqrt> <mrow> <mi mathvariant="monospace">S</mi> <mo>(</mo> <mi>ν</mi> <mo>)</mo> </mrow> </msqrt> </semantics></math> of different GW detectors along with <math display="inline"><semantics> <mrow> <msqrt> <mrow> <mi mathvariant="script">T</mi> <mo>/</mo> <mn>5</mn> </mrow> </msqrt> <mi>h</mi> </mrow> </semantics></math> for the various rotating magnetized WDs with different integration times. We assume <math display="inline"><semantics> <mrow> <mi>χ</mi> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> pc. The typical masses of the WDs are 1.40–2.65 <math display="inline"><semantics> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </semantics></math> with radii ∼ 750–3300 km, <math display="inline"><semantics> <mrow> <msub> <mi>I</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <mo>∼</mo> <msup> <mn>10</mn> <mn>48</mn> </msup> </mrow> </semantics></math>–<math display="inline"><semantics> <msup> <mn>10</mn> <mn>49</mn> </msup> </semantics></math> g cm<math display="inline"><semantics> <msup> <mrow/> <mn>2</mn> </msup> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>∼</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math>–<math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> depending on <math display="inline"><semantics> <msub> <mi>ρ</mi> <mi>c</mi> </msub> </semantics></math>, magnetic field geometry and its strength.</p>
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<p>Variation of <span class="html-italic">P</span>, <math display="inline"><semantics> <mi>χ</mi> </semantics></math>, <math display="inline"><semantics> <msub> <mi>L</mi> <mi mathvariant="normal">D</mi> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>L</mi> <mi>GW</mi> </msub> </semantics></math> with respect to time.</p>
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1648 KiB  
Proceeding Paper
A Data Driven Approach to the Measurement of 10Be/9Be in Cosmic Rays with Magnetic Spectrometers
by Cinzia Cernetti and Francesco Nozzoli
Phys. Sci. Forum 2021, 2(1), 13; https://doi.org/10.3390/ECU2021-09273 - 22 Feb 2021
Viewed by 1246
Abstract
Cosmic Rays (CRs) are powerful tools for the investigation of the structure of the magnetic fields in the galactic halo and the properties of the Inter-Stellar Medium. There are two parameters of CR propagation models: The galactic halo (half-) thickness, H, and [...] Read more.
Cosmic Rays (CRs) are powerful tools for the investigation of the structure of the magnetic fields in the galactic halo and the properties of the Inter-Stellar Medium. There are two parameters of CR propagation models: The galactic halo (half-) thickness, H, and the diffusion coefficient, D, are loosely constrained by current CR flux measurements; in particular, a large degeneracy exists, as only H/D is well measured. The 10Be/9Be isotopic flux ratio (thanks to the 2 My lifetime of 10Be) can be used as a radioactive clock that provides the measurement of the residence time of CRs in the galaxy. This is an important tool for solving the degeneracy of H/D. Past measurements of the 10Be/9Be isotopic flux ratios in CRs are scarce, limited to low energy, and affected by large uncertainties. Here, a new technique for measuring the 10Be/9Be isotopic flux ratio in magnetic spectrometers with a data-driven approach is presented. As an example, by applying the method to beryllium events that were published by the PAMELA experiment, it is now possible to determine the important 10Be/9Be measurements while avoiding the prohibitive uncertainties coming from Monte Carlo simulations. It is shown how the accuracy of the PAMELA data permits one to infer a value of the halo thickness with a precision of up to 25%. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Unbiased map of the <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> configurations for PAMELA–ToF in the 0.65–0.85 GeV/n region.</p>
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<p>Example of the measurement of beryllium isotopes with the data-driven analysis of the PAMELA–ToF data collected in the 0.65–0.85 GeV/n range.</p>
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<p>Comparison of the results of the data-driven analysis for <math display="inline"><semantics> <msup> <mrow/> <mn>10</mn> </msup> </semantics></math>Be/<math display="inline"><semantics> <msup> <mrow/> <mn>9</mn> </msup> </semantics></math>Be and <math display="inline"><semantics> <msup> <mrow/> <mn>7</mn> </msup> </semantics></math>Be fraction with those of previous experiments and a Monte-Carlo-based analysis. Statistic error bars are only drawn for the data-driven analysis results.</p>
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770 KiB  
Proceeding Paper
“Null String” Gas Cosmology: 1st Steps
by Alexander Lelyakov
Phys. Sci. Forum 2021, 2(1), 14; https://doi.org/10.3390/ECU2021-09330 - 23 Feb 2021
Viewed by 3328
Abstract
This work is devoted to the study of the asymptotics of the gravitational field of primary particles with nonzero rest mass. These particles are structurally composed of two closed “null strings” (thin closed tubes of a massless scalar field) in the shape of [...] Read more.
This work is devoted to the study of the asymptotics of the gravitational field of primary particles with nonzero rest mass. These particles are structurally composed of two closed “null strings” (thin closed tubes of a massless scalar field) in the shape of a circle, and they are formed in a gas of null strings as a result of gravitational interaction. It is shown that on time scales much larger than the time of one complete cycle of oscillation of the null strings forming a particle, or at distances much larger than the dimensions of the region within which the oscillations of interacting null strings occur, the gravitational field of such a particle is described by the Minkowski metric. It is noted that with decreasing observation time or on distance scales that are commensurate with the size of primary particles, significant deviations of the gravitational field from the flat Minkowski space-time should appear in the gas of null strings. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>The figure shows an example of the trajectories of motion of two null strings forming a primary particle, the meeting surface for which is orthogonal to the <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> axis (<math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msub> <mi>R</mi> <mn>0</mn> </msub> </mrow> </semantics></math>).</p>
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<p>The figure shows an example of the trajectories of motion of two null strings forming a primary particle, the meeting surface for which is orthogonal to the <math display="inline"><semantics> <mi>Z</mi> </semantics></math> axis (<math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> </mrow> </semantics></math>).</p>
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<p>In the figure (<b>a</b>,<b>b</b>), two possibilities of combining gravitationally-interacting null strings into a spherically symmetric domain are schematically presented.</p>
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3211 KiB  
Proceeding Paper
Moon Mapping Project Results on Solar Wind ion Flux and Composition
by Francesco Nozzoli and Pietro Richelli
Phys. Sci. Forum 2021, 2(1), 16; https://doi.org/10.3390/ECU2021-09327 - 23 Feb 2021
Viewed by 1646
Abstract
The “Moon Mapping” project is a collaboration between the Italian and Chinese Governments allowing cooperation and exchange from students from both countries. Main aim of the project is to analyze remotely sensed data collected by the Chinese space missions Chang’E-1/2 over the Moon [...] Read more.
The “Moon Mapping” project is a collaboration between the Italian and Chinese Governments allowing cooperation and exchange from students from both countries. Main aim of the project is to analyze remotely sensed data collected by the Chinese space missions Chang’E-1/2 over the Moon surface. The Italian Space Agency is responsible for the Italian side and the Center of Space Exploration, China Ministry of Education, is responsible for the Chinese side. The results of the “Moon Mapping” project topic #1: ”map of the solar wind ion” using data collected by Chang’E-1 satellite are summarized. Chang’E-1 is a lunar orbiter, the revolution period is 2 h and the orbit is polar. The satellite is equipped with two Solar Wind Ion Detectors (SWIDs) that are two perpendicular electrostatic spectrometers mapping the sky with 24 channels with a field of view of 15° × 6.7° each. The spectrometers can measure solar wind flux in the range 40 eV/q–17 keV/q with an energy resolution of 8%. The data collected by the two Solar Wind Ion Detectors are analyzed to characterize the solar wind flux and composition on the Moon surface, studying the large time variation due to the solar activity. The data measured by Chang’E-1, as compared with the one measured in the same period by the electrostatic spectrometers onboard the ACE satellite, enrich the multi-messenger/multi-particle view of the Sun, gathering valuable information about the space weather outside the Earth’s magnetosphere. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Basic principle diagram of SWID. The orbit of the Chang’E-1 spacecraft allows scaning a large fraction of the sky in the field of view of the SWIDs.</p>
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<p>Basic principle diagram of SWID. The orbit of the Chang’E-1 spacecraft allows scaning a large fraction of the sky in the field of view of the SWIDs.</p>
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<p>Sun centered solar wind flux map as measured by Chang’E-1. The apparent angular size of the Sun in this map is compatible with the 15° FWHM angular aperture of the Chang’E-1 SWID channels.</p>
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<p>Solar wind flux measured by Chang’E−1 as a function of time and kinetic energy. The time variation of the average kinetic energy are in good correlation with the measured solar wind velocity by ACE (red dots).</p>
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<p>Top plot: typical solar wind energy distribution measured by SWIDs. Bottom plot: relative abundances of He<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </semantics></math> (red) and heavier ions (blue) measured during Chang’E−1 mission.</p>
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<p>Top plot: typical solar wind energy distribution measured by SWIDs. Bottom plot: relative abundances of He<math display="inline"><semantics> <msup> <mrow/> <mrow> <mo>+</mo> <mo>+</mo> </mrow> </msup> </semantics></math> (red) and heavier ions (blue) measured during Chang’E−1 mission.</p>
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381 KiB  
Proceeding Paper
Casimir Effect as a Probe for New Physics Phenomenology
by Luciano Petruzziello
Phys. Sci. Forum 2021, 2(1), 17; https://doi.org/10.3390/ECU2021-09307 - 22 Feb 2021
Viewed by 1477
Abstract
We show some recent cutting-edge results associated with the Casimir effect. Specifically, we focused our attention on the remarkable sensitivity of the Casimir effect to new physics phenomenology. Such an awareness can be readily discerned by virtue of the existence of extra contributions [...] Read more.
We show some recent cutting-edge results associated with the Casimir effect. Specifically, we focused our attention on the remarkable sensitivity of the Casimir effect to new physics phenomenology. Such an awareness can be readily discerned by virtue of the existence of extra contributions that the measurable quantities (such as the emergent pressure and strength within the experimental apparatus) acquire for a given physical setting. In particular, by relying on the above framework, we outlined the possibility of detecting the predictions of a novel quantum field theoretical description for particle mixing according to which the flavor and the mass vacuum are unitarily non-equivalent. Furthermore, by extending the very same formalism to curved backgrounds, the opportunity to probe extended models of gravity that encompass local Lorentz symmetry breaking and the strong equivalence principle violation was also discussed. Finally, the influence of quantum gravity on the Casimir effect was briefly tackled by means of heuristic considerations. In a similar scenario, the presence of a minimal length at the Planck scale was the source of the discrepancy with the standard outcomes. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>In this figure, the Casimir apparatus is displayed.</p>
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<p>In this figure, the Casimir apparatus in curved spacetime is exhibited.</p>
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217 KiB  
Proceeding Paper
Accuracy of an EGB Exponential Inflationary Scenario
by Ekaterina Pozdeeva
Phys. Sci. Forum 2021, 2(1), 20; https://doi.org/10.3390/ECU2021-09294 - 22 Feb 2021
Viewed by 1109
Abstract
Earlier we constructed a model with exponential form potential and of Gauss–Bonnet interaction. This model can be considered as an appropriate inflationary scenario. In this model, the attractor inflationary parameters correspond to ones from the cosmological attractor model in leading order approximation in [...] Read more.
Earlier we constructed a model with exponential form potential and of Gauss–Bonnet interaction. This model can be considered as an appropriate inflationary scenario. In this model, the attractor inflationary parameters correspond to ones from the cosmological attractor model in leading order approximation in an inverse e-folding number. We study how many orders of inverse e-folding numbers are included in the spectral index in exponential inflationary scenario in the Einstein–Gauss–Bonnet gravity. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
7 pages, 2737 KiB  
Proceeding Paper
Gravity Variation Effects on the Growth of Maize Shoots
by Funmilola Oluwafemi
Phys. Sci. Forum 2021, 2(1), 21; https://doi.org/10.3390/ECU2021-10184 - 27 May 2021
Viewed by 2266
Abstract
Gravity variation effects on plants provide definite changes. Normal Earth gravity (1G) and microgravity (µg) are possible variations for experimental purposes. On-board spaceflight microgravity experiments are rare and expensive, as the microgravity environment is an outstanding platform for research, application and education. A [...] Read more.
Gravity variation effects on plants provide definite changes. Normal Earth gravity (1G) and microgravity (µg) are possible variations for experimental purposes. On-board spaceflight microgravity experiments are rare and expensive, as the microgravity environment is an outstanding platform for research, application and education. A Clinostat was used for ground-based experiments to investigate the shoot morphology of maize plants at the Space Agency of Nigeria—National Space Research and Development Agency (NASRDA). A Clinostat device uses rotation to negate gravitational pull effects on plant growth and development. Maize was selected for this experiment because of its nutritional and economic importance, and its usability on the Clinostat. Plant shoot morphology is important for gravi-responses. Shoot curvature and shoot growth rate analyses were conducted on the shoots of a provitamin variety of maize. The seeds were planted into three Petri dishes (in parallel) in a wet chamber using a plant substrate—agar-agar. The experimental conditions were subject to relative humidity, temperature and light conditions. After 3 days of germination under 1G, two of the Petri dishes were left under 1G, serving as controls for shoot curvature and shoot growth rate analyses. The clinorotated sample was mounted on the Clinostat under: a fast rotation speed of 80 rpm, a horizontal rotation position and a clockwise rotation direction. The images of the samples were taken at a 30 min interval for 4 h. After observations, the shoot morphology of the seedlings was studied using ImageJ software. The grand average shoot angles and shoot lengths of all the seedlings were calculated following the experimental period to provide the shoot curvatures and shoot growth rates, respectively. The results show that the clinorotated sample had a reduced response to gravity, with 50.77°/h for the shoot curvature, while the 90°-turned sample had 55.49°/h. The shoot growth rate for the 1G sample was 1.25 cm/h, while that for the clinorotated sample was 1.26 cm/h. The clinorotated sample had an increased growth rate per hour compared to the counterpart 1G sample. These analytical results serve as preparation for future real-space experiments on maize and could be beneficial to the agriculture sector. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>2-D Clinostat at the Microgravity Simulations Laboratory, National Space Research and Development Agency (NASRDA), Abuja, Nigeria.</p>
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<p>The maize seeds in the wet chamber for cultivation.</p>
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<p>The three samples: (<b>a</b>) 1G-control sample; (<b>b</b>) 90°-turned sample; (<b>c</b>) clinorotated sample.</p>
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<p>Shoot length (cm) of the 1G-control and the clinorotated samples of maize seedlings against the time (h).</p>
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<p>Shoot curvature of the 90°-turned and the clinorotated samples of maize seedlings.</p>
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400 KiB  
Proceeding Paper
Stable, Spherical and Thin Fluid Shells
by George Alestas, George V. Kraniotis and Leandros Perivolaropoulos
Phys. Sci. Forum 2021, 2(1), 24; https://doi.org/10.3390/ECU2021-09332 - 24 Feb 2021
Viewed by 1560
Abstract
We consider and prove the existence of stable, spherical, and thin fluid shells in the context of a Schwarzschild–Rindler-anti-de Sitter (SRAdS) background. We identify the metric parameter regions that allow the existence and stability of these shells for three cases of fluid equations [...] Read more.
We consider and prove the existence of stable, spherical, and thin fluid shells in the context of a Schwarzschild–Rindler-anti-de Sitter (SRAdS) background. We identify the metric parameter regions that allow the existence and stability of these shells for three cases of fluid equations of state. The case of the vacuum shell is especially interesting since it remains consistent with past studies by two of the authors of this manuscript, which showed the existence of stable spherical domain walls in the context of the same metric. This type of structure could be an alternative to the idea of the gravastar star formations. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>We see how the stability regions (light blue region) vary for two cases of exterior masses of the shell. Each of the different colored curves correspond to different values of the surface density <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>0</mn> </msub> <mo>≡</mo> <msub> <mi>σ</mi> <mrow> <mn>0</mn> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mo>Δ</mo> <mi>σ</mi> <mo>&gt;</mo> <msub> <mi>σ</mi> <mrow> <mn>0</mn> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math>. The left panel corresponds to <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mo>+</mo> </msub> <mo>=</mo> <mn>1.05</mn> </mrow> </semantics></math> and the right to <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mo>+</mo> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math>.</p>
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<p>The potential (<a href="#FD15-psf-02-00024" class="html-disp-formula">15</a>) for the values of <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>b</mi> <mo>,</mo> <mo>Λ</mo> <mo>)</mo> </mrow> </semantics></math> that correspond to the points highlighted in <a href="#psf-02-00024-f001" class="html-fig">Figure 1</a>. We see that the red point of <a href="#psf-02-00024-f001" class="html-fig">Figure 1</a> does not correspond to a stable shell solution.</p>
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<p>A random Monte Carlo selection of points that satisfy the shell existence and stability conditions (<a href="#FD18-psf-02-00024" class="html-disp-formula">18</a>)–(<a href="#FD21-psf-02-00024" class="html-disp-formula">21</a>) for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mo>+</mo> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math>. The orange line represents the limit of the region, which is clearly respected by all the randomly selected points, which span the stability region.</p>
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342 KiB  
Proceeding Paper
Second Order Glauber Correlation of Gravitational Waves Using the LIGO Observatories as Hanbury Brown and Twiss Detectors
by Alexander Barrett and Preston Jones
Phys. Sci. Forum 2021, 2(1), 25; https://doi.org/10.3390/ECU2021-09519 - 19 Mar 2021
Viewed by 2117
Abstract
The second order Glauber correlation of a simplified gravitational wave is investigated, using parameters from the first signal detected by LIGO. This simplified model spans the inspiral, merger, and ringdown phases of a black hole merger and was created to have a continuous [...] Read more.
The second order Glauber correlation of a simplified gravitational wave is investigated, using parameters from the first signal detected by LIGO. This simplified model spans the inspiral, merger, and ringdown phases of a black hole merger and was created to have a continuous amplitude, so there is no discontinuity between the phases. This allows for a trivial extraction of the intensity, which is necessary for determining the correlation between detectors. The two LIGO observatories can be used as detectors in a Hanbury Brown and Twiss interferometer for gravitational waves; these observatories measure the amplitude of the wave, so these measurements were used as the basis of the simplified model. The signal detected by the observatories is transient and is not consistent with chaotic or steady electromagnetic waves and thus the second order Glauber correlation function was calculated to produce physically meaningful results. To find correlations that are consistent with applications to electromagnetic waves, weighting functions for both models were studied in the integral equations for the Glauber correlation functions. The relationship between the transient and chaotic signals of both waveforms and their respective correlation functions was also examined. The second order Glauber correlation functions are a measure of intensity interference between independent detectors and has proven to be useful in both optics and particle physics. It has also been used in theoretical studies of primordial gravitational waves. The correlations can be used to define the degrees of coherence of a field, characterize multi-particle processes and assist in image enhancement. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Glauber correlation function of (<a href="#FD8-psf-02-00025" class="html-disp-formula">8</a>) generated by (<a href="#FD11-psf-02-00025" class="html-disp-formula">11</a>).</p>
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<p>Glauber correlation of (<a href="#FD8-psf-02-00025" class="html-disp-formula">8</a>) generated by (<a href="#FD3-psf-02-00025" class="html-disp-formula">3</a>).</p>
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<p>Model gravitational wave waveform from Equation (<a href="#FD13-psf-02-00025" class="html-disp-formula">13</a>).</p>
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<p>Glauber correlation of (<a href="#FD13-psf-02-00025" class="html-disp-formula">13</a>) generated by (<a href="#FD11-psf-02-00025" class="html-disp-formula">11</a>).</p>
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<p>Glauber correlation of (<a href="#FD13-psf-02-00025" class="html-disp-formula">13</a>) generated by (<a href="#FD3-psf-02-00025" class="html-disp-formula">3</a>).</p>
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268 KiB  
Proceeding Paper
Effects of Higher Order Retarded Gravity on Galaxies
by Asher Yahalom
Phys. Sci. Forum 2021, 2(1), 26; https://doi.org/10.3390/ECU2021-09328 - 23 Feb 2021
Cited by 1 | Viewed by 2174
Abstract
In a recent paper, we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this relies on a temporal change of galactic mass. In our previous work, we kept only second order terms of the retardation [...] Read more.
In a recent paper, we have a shown that the flattening of galactic rotation curves can be explained by retardation. However, this relies on a temporal change of galactic mass. In our previous work, we kept only second order terms of the retardation time in our analysis, while higher terms in the Taylor expansion were not considered. Here, we consider analysis to all orders and show that, indeed, a second order analysis will suffice, and higher order terms can be neglected. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
7360 KiB  
Proceeding Paper
Magnetized Black Hole as an Accelerator of Charged Particle
by Bobur Turimov
Phys. Sci. Forum 2021, 2(1), 27; https://doi.org/10.3390/ECU2021-09303 - 22 Feb 2021
Viewed by 1668
Abstract
Astrophysical accretion processes near the black hole candidates, such as active galactic nuclei (AGN), X-ray binary (XRB), and other astrophysical sources, are associated with high-energetic emission of radiation of relativistic particles and outflows (winds or jets). It is widely believed that the magnetic [...] Read more.
Astrophysical accretion processes near the black hole candidates, such as active galactic nuclei (AGN), X-ray binary (XRB), and other astrophysical sources, are associated with high-energetic emission of radiation of relativistic particles and outflows (winds or jets). It is widely believed that the magnetic field plays a very important role to explain such high energetic processes in the vicinity of those astrophysical sources. In the present research note, we propose that the black hole is embedded in an asymptotically uniform magnetic field. We investigate the dynamic motion of charged particles in the vicinity of a weakly magnetized black hole. We show that, in the presence of the magnetic field, the radius of the innermost stable circular orbits (ISCO) for a charged particle is located close to the black hole’s horizon. The fundamental frequencies, such as Keplerian and epicyclic frequencies of the charged particle are split into two parts due to the magnetic field, as an analog of the Zeeman effect. The orbital velocity of the charged particle measured by a local observer has been computed in the presence of the external magnetic field. We also present an analytical expression for the four-acceleration of the charged particle orbiting around black holes. Finally, we determine the intensity of the radiating charged accelerating relativistic particle orbiting around the magnetized black hole. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Dependence the ISCO and MBO radii from the magnetic coupling parameter <math display="inline"><semantics> <mrow> <mi>q</mi> <mi>B</mi> <mi>M</mi> <mo>/</mo> <mi>m</mi> </mrow> </semantics></math> for the positively and negatively charged particle.</p>
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<p>Dependence the energy efficiency from the magnetic coupling parameter <math display="inline"><semantics> <mrow> <mi>q</mi> <mi>B</mi> <mi>M</mi> <mo>/</mo> <mi>m</mi> </mrow> </semantics></math> for the positively and negatively charged particle.</p>
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<p>The trajectory of charged particle around magnetized black hole.</p>
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<p>Radial dependence of the fundamental frequencies for positive <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>B</mi> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, zero <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>B</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and negative <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>B</mi> </msub> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> values of the interaction parameter. The gray line represents Keplerian frequency, while the blue and red lines are responsible frequencies for the radial and vertical oscillations, respectively.</p>
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285 KiB  
Proceeding Paper
An Overview of Nonstandard Signals in Cosmological Data
by George Alestas, George V. Kraniotis and Leandros Perivolaropoulos
Phys. Sci. Forum 2021, 2(1), 28; https://doi.org/10.3390/ECU2021-09333 - 25 Feb 2021
Viewed by 1635
Abstract
We discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension (2σ or larger) with the standard ΛCDM as defined by the Planck18 parameter values. The well known tensions of [...] Read more.
We discuss in a unified manner many existing signals in cosmological and astrophysical data that appear to be in some tension (2σ or larger) with the standard ΛCDM as defined by the Planck18 parameter values. The well known tensions of ΛCDM include the H0 tension the S8 tension and the lensing (Alens) CMB anomaly. There is however, a wide range of other, less standard signals towards new physics. Such signals include, hints for a closed universe in the CMB, the cold spot anomaly indicating non-Gaussian fluctuations in the CMB, the hemispherical temperature variance assymetry and other CMB anomalies, cosmic dipoles challenging the cosmological principle, the Lyman-α forest Baryon Accoustic Oscillation anomaly, the cosmic birefringence in the CMB, the Lithium problem, oscillating force signals in short range gravity experiments etc. In this contribution present the current status of many such signals emphasizing their level of significance and referring to recent resources where more details can be found for each signal. We also briefly mention some possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. In many cases, the signals presented are controversial and there is currently debate in the literature on the possible systematic origin of some of these signals. However, for completeness we refer to all the signals we could identify in the literature citing also references that dispute their physical origin. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
591 KiB  
Proceeding Paper
Role of Anisotropy on the Tidal Deformability of Compact Stellar Objects
by Shyam Das, Bikram Keshari Parida, Saibal Ray and Shyamal Kumar Pal
Phys. Sci. Forum 2021, 2(1), 29; https://doi.org/10.3390/ECU2021-09311 - 22 Feb 2021
Cited by 5 | Viewed by 1623
Abstract
In this paper, we introduce a framework to study the tidal deformation of relativistic anisotropic compact stars. Anisotropic stresses are ubiquitous in nature and widely used in modelling compact stellar objects. Tidal deformability of astrophysical compact objects is a natural effect of gravity, [...] Read more.
In this paper, we introduce a framework to study the tidal deformation of relativistic anisotropic compact stars. Anisotropic stresses are ubiquitous in nature and widely used in modelling compact stellar objects. Tidal deformability of astrophysical compact objects is a natural effect of gravity, such as one produced by a companion in a binary system. In general relativity, the existence of this measurable effect of gravity can be quantified by their tidal Love numbers (TLN), which characterize the deformability of a neutron star (NS) from sphericity. The tidal deformability or polarizability parameter of an NS depends on its complex internal structure, and hence, the nature of the compact object can be studied by measuring the TLN. We choose a particular solution, which is the anisotropic generalization of the Tolman IV model, as the interior of the compact stellar object. The physical acceptability of the model has been shown graphically by considering the pulsar 4U 1608-52 with their current estimated mass and radius. By computing the quadrupole moment, we found that the TLN is dependent on anisotropy of the compact object. We graphically analyze the variation of the TLN against anisotropy for different compact objects with a compactness factor. The numerical value of TLN is given for different compact objects for physically acceptable values of the anisotropic parameter. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Physical features are plotted against the radial parameter for the compact star 4U 1608-52.</p>
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<p><math display="inline"><semantics> <msub> <mi>k</mi> <mn>2</mn> </msub> </semantics></math> is plotted against <math display="inline"><semantics> <mi>α</mi> </semantics></math> for different compact objects with compactness <math display="inline"><semantics> <mi mathvariant="script">C</mi> </semantics></math> only for the allowed values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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266 KiB  
Proceeding Paper
A Proposal for Introducing Quantum Physics in the Footsteps of Einstein
by Marco Di Mauro, Salvatore Esposito and Adele Naddeo
Phys. Sci. Forum 2021, 2(1), 30; https://doi.org/10.3390/ECU2021-09320 - 22 Feb 2021
Cited by 1 | Viewed by 1635
Abstract
We formulate a didactic proposal for introducing some fundamental concepts of quantum physics to advanced high school students, and to their teachers. The inspiration comes from some of the fundamental papers about the subject by Albert Einstein, in which many of these concepts, [...] Read more.
We formulate a didactic proposal for introducing some fundamental concepts of quantum physics to advanced high school students, and to their teachers. The inspiration comes from some of the fundamental papers about the subject by Albert Einstein, in which many of these concepts, for example light quanta, wave-particle duality, and probability, were introduced for the first time, in a characteristically illuminating way. The proposal can be supplemented by a discussion of elementary tools of statistical physics, which are needed at some point. Preliminary results, both with students and teachers, are very promising. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
249 KiB  
Proceeding Paper
Effects of Baryon-Antibaryon Annihilation in the Evolution of Antimatter Domains in Baryon Asymmetrical Universe
by Maxim Yu. Khlopov and Orchidea Maria Lecian
Phys. Sci. Forum 2021, 2(1), 31; https://doi.org/10.3390/ECU2021-09267 - 22 Feb 2021
Cited by 1 | Viewed by 1391
Abstract
The mechanisms of baryosynthesis, which involve the three Sakharov’s conditions, admit a possibility of nonhomogeneous generation of baryon excess. It may take place in the case of spatial variation of CP violating phase or of the baryon generating field in the early Universe. [...] Read more.
The mechanisms of baryosynthesis, which involve the three Sakharov’s conditions, admit a possibility of nonhomogeneous generation of baryon excess. It may take place in the case of spatial variation of CP violating phase or of the baryon generating field in the early Universe. In the extreme case this nonhomogeneity can lead to the change of sign of baryon excess and formation of antibaryon domains in baryon asymmetrical Universe. Surrounded by the baryon matter, evolution of antibaryon domains is strongly influenced by effect of baryon and antibaryon diffusion to the border of domain and their annihilation. It leads to change of size of domains and antibaryon density in them. The consequence of antibaryon-baryon annihilation at the border of antimatter domains in baryon-asymmetrical Universe is investigated. The successive evolution in the expanding Universe strongly depends on antibaryon density within domain. At low density it is not sufficient to provide separation from cosmological expansion. Such separation can, however, be provided by effects of dark matter, which we briefly discuss. Low-density antimatter domains are further classified with the account for the border interactions. Differently, a similar classification scheme is also proposed for higher-densities antimatter domains. The effects of antinuclei-nuclei-interaction-patterns are investigated and taken into account in the analysis of antimatter domain evolution. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
715 KiB  
Proceeding Paper
Gravitation in the Space with Chimney Topology
by Maxim Eingorn, Andrew McLaughlin II, Ezgi Canay, Maksym Brilenkov and Alexander Zhuk
Phys. Sci. Forum 2021, 2(1), 32; https://doi.org/10.3390/ECU2021-09295 - 22 Feb 2021
Cited by 1 | Viewed by 1310
Abstract
Searching for possible indicators of spatial topology of the Universe in the Cosmic Microwave Background data, one recognizes a quite promising interpretation which suggests that the shape of the space manifests itself in the form of anomalies in the large angular scale observations, [...] Read more.
Searching for possible indicators of spatial topology of the Universe in the Cosmic Microwave Background data, one recognizes a quite promising interpretation which suggests that the shape of the space manifests itself in the form of anomalies in the large angular scale observations, such as the quadrupole and octopole alignment. Motivated by the presumptive existence of such a tempting connection, we study the chimney topology, T×T×R, which belongs to the class of toroidal topologies with a preferred direction. The infinite axis in this case may be attributed to the preferred axis of the aforementioned quadrupole and octopole alignment. We investigate the gravitational aspects of such a configuration. Namely, we reveal the form of the gravitational potential sourced by point-like massive bodies. Starting from the perturbed Einstein equations, which ensure the proper demonstration of relativistic effects, one can derive the Helmholtz equation for the scalar perturbation (gravitational potential). Through distinct alternative methods, we present the physically meaningful nontrivial exact solutions of this equation. Our approach excludes any presumptions regarding the spatial distribution of gravitating sources. We show that the particular solution that appears in the form of summed Yukawa potentials is indeed very convenient for the use in numerical calculations, in the sense that it provides the desired accuracy with fewer terms in the series. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Rescaled gravitational potential <math display="inline"><semantics> <mrow> <mover accent="true"> <mi mathvariant="sans-serif">Φ</mi> <mo>˜</mo> </mover> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (<b>a</b>) for <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>λ</mi> <mo>˜</mo> </mover> <mrow> <mi>eff</mi> </mrow> </msub> </mrow> </semantics></math> = 0.01; (<b>b</b>) for <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>λ</mi> <mo>˜</mo> </mover> <mrow> <mi>eff</mi> </mrow> </msub> </mrow> </semantics></math> = 0.1.</p>
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Proceeding Paper
Dark Matter Annual Modulation Results from the ANAIS-112 Experiment
by Julio Amaré, Susana Cebrián, David Cintas, Iván Coarasa, Eduardo García, María Martínez, Miguel Ángel Oliván, Ysrael Ortigoza, Alfonso Ortiz de Solórzano, Jorge Puimedón, Ana Salinas, María Luisa Sarsa and Patricia Villar
Phys. Sci. Forum 2021, 2(1), 33; https://doi.org/10.3390/ECU2021-09331 - 24 Feb 2021
Viewed by 2292
Abstract
An annual modulation in the interaction rate of galactic dark matter particles is foreseen due to Earth’s movement around the Sun; the DAMA/LIBRA observation of a modulation signal compatible with expectations has intrigued the community for twenty years. The ANAIS-112 experiment, with a [...] Read more.
An annual modulation in the interaction rate of galactic dark matter particles is foreseen due to Earth’s movement around the Sun; the DAMA/LIBRA observation of a modulation signal compatible with expectations has intrigued the community for twenty years. The ANAIS-112 experiment, with a target of 112.5 kg of NaI(Tl), has been running smoothly at the Canfranc Underground Laboratory (Spain) since 2017. It aims to test this observation using the same detection technique and target. Results on the modulation search from two years of data (220.7 kg·y) have been presented and the analysis of three years (313.6 kg·y) is underway. Under the hypothesis of modulation, the deduced amplitudes from best fits are in all cases compatible with zero for the two energy regions at [2–6] and [1–6] keV; the results agree with the expected sensitivity for the considered exposure and fully support the goal of achieving a 3σ sensitivity to explore the DAMA/LIBRA result for a five-year operation. Here, the ANAIS-112 set-up and performance will be briefly recapped and the annual modulation results and prospects will be discussed. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Set-up of the ANAIS-112 experiment: (<b>a</b>) Schematic view showing the nine modules and the full shielding; (<b>b</b>) Picture taken during ANAIS-112 commissioning with detectors, lead shielding and calibration system visible.</p>
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<p>Results of the fit of ANAIS-112 data for first 2 years to Equation (1) in the two energy regions of [1–6] and [2–6] keV in the modulation (blue) and null hypothesis (red). The non-modulated components were subtracted after fitting. DAMA/LIBRA results are shown too (in green) for comparison.</p>
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<p>Comparison between ANAIS-112 best fit for the annual modulation amplitude S<sub>m</sub> from the first 2 years of data and DAMA/LIBRA result [<a href="#B3-psf-02-00033" class="html-bibr">3</a>], for the two considered energy regions. The estimated sensitivity is presented too at several confidence levels as coloured bands: 1σ (green), 2σ (yellow) and 3σ (cyan).</p>
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<p>ANAIS-112 sensitivity to DAMA/LIBRA signal in units of σ C.L. as a function of time. Cyan bands show the 68% C.L. DAMA/LIBRA uncertainty in the modulation amplitude. Black dots and numbers gave the experimental sensitivities obtained in the two ANAIS-112 annual modulation analysis carried out for 1.5 and 2 years.</p>
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Proceeding Paper
Dynamics of Disk and Elliptical Galaxies in Refracted Gravity
by Valentina Cesare
Phys. Sci. Forum 2021, 2(1), 34; https://doi.org/10.3390/ECU2021-09292 - 22 Feb 2021
Cited by 2 | Viewed by 1249
Abstract
I investigate the dynamics of galaxies in refracted gravity (RG), a novel theory of modified gravity which does not resort to dark matter (DM). The DM presence is mimicked by a gravitational permittivity, a monotonic increasing function of the local mass density that [...] Read more.
I investigate the dynamics of galaxies in refracted gravity (RG), a novel theory of modified gravity which does not resort to dark matter (DM). The DM presence is mimicked by a gravitational permittivity, a monotonic increasing function of the local mass density that depends on three, in principle, universal parameters. RG reproduces the kinematic profiles of 30 disk galaxies in the DiskMass Survey (DMS), with mass-to-light ratios in agreement with stellar population synthesis models, disk-scale heights consistent with edge-on galaxies observations, and the RG parameters from the individual galaxies in agreement with one another, suggesting their universality. RG models the radial acceleration relation of the DMS galaxies with the correct asymptotic limits but with residuals correlating with some galaxies properties and with a too large intrinsic scatter, in contrast with observations, which requires further investigation. RG also describes the velocity dispersions of stars and of blue and red globular clusters in three elliptical E0 galaxies from the SLUGGS survey with sensible mass-to-light ratios and anisotropy parameters and with the three RG parameters consistent with one another. These parameters are also in agreement with the mean RG parameters estimated from the individual DMS galaxies. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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Proceeding Paper
Position in Models of Quantum Mechanics with a Minimal Length
by Pasquale Bosso
Phys. Sci. Forum 2021, 2(1), 35; https://doi.org/10.3390/ECU2021-09275 - 22 Feb 2021
Cited by 1 | Viewed by 1540
Abstract
Candidate theories of quantum gravity predict the presence of a minimal measurable length at high energies. Such feature is in contrast with the Heisenberg Uncertainty Principle. Therefore, phenomenological approaches to quantum gravity introduced models spelled as modifications of quantum mechanics including a minimal [...] Read more.
Candidate theories of quantum gravity predict the presence of a minimal measurable length at high energies. Such feature is in contrast with the Heisenberg Uncertainty Principle. Therefore, phenomenological approaches to quantum gravity introduced models spelled as modifications of quantum mechanics including a minimal length. The effects of such modification are expected to be relevant at large energies/small lengths. One first consequence is that position eigenstates are not included in such models due to the presence of a minimal uncertainty in position. Furthermore, depending on the particular modification of the position–momentum commutator, when such models are considered from momentum space, the position operator is changed, and a measure factor appears to let the position operator be self-adjoint. As a consequence, the (quasi-)position representation acquires numerous issues. For example, the position operator is no longer a multiplicative operator, and the momentum of a free particle does not correspond directly to its wave number. Here, we will review such issues, clarifying aspects of minimal length models, with particular reference to the representation of the position operator. Furthermore, we will show how such a (quasi-)position description of quantum mechanical models with a minimal length affects results concerning simple systems. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Energy times mass of a particle in a box of width 1 m. The green line represents the ordinary case, and the blue and orange lines represent two different GUP parametrizations. The dashed vertical lines represent the maximum integer n allowed for that particular model.</p>
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<p>Resonance energies with a minimal length (blue and orange dots) and in the standard case (green dots). The vertical lines represent the maximum number of resonances allowed in the models. Here, a barrier of width <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>20</mn> <msub> <mi>l</mi> <mrow> <mi>P</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> and height <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>120</mn> <msup> <mo>ℏ</mo> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>mL</mi> <mn>2</mn> </msup> </mrow> </semantics></math> has been used.</p>
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<p>Transmission coefficient as a function of the ratio between the energy of the incoming wave and the barrier height. Here, a barrier of width <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>1</mn> <msub> <mi>l</mi> <mrow> <mi>P</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> and height <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>120</mn> <msup> <mo>ℏ</mo> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>mL</mi> <mn>2</mn> </msup> </mrow> </semantics></math> has been used. It is worth noticing that the transmission coefficient is equal to 1, or close to 1, even when <math display="inline"><semantics> <mrow> <mi>E</mi> <mo>&lt;</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> </mrow> </semantics></math>.</p>
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256 KiB  
Proceeding Paper
Bianchi Type I Cosmological Model in f(R,T) Gravity
by Rishi Kumar Tiwari, Aroonkumar Beesham, Soma Mishra and Vipin Dubey
Phys. Sci. Forum 2021, 2(1), 38; https://doi.org/10.3390/ECU2021-09290 - 22 Feb 2021
Cited by 3 | Viewed by 1617
Abstract
Although the present universe is believed to be homogeneous and isotropic on large scales, there is some evidence of some anisotropy at early times. Hence, there is interest in the Bianchi models, which are homogeneous but anisotropic. In this presentation, the Bianchi type–I [...] Read more.
Although the present universe is believed to be homogeneous and isotropic on large scales, there is some evidence of some anisotropy at early times. Hence, there is interest in the Bianchi models, which are homogeneous but anisotropic. In this presentation, the Bianchi type–I space-time in the framework of the f(R,T) modified theory of gravity has been investigated for the specific choice of f(R,T) = R + 2f(T), where f(T) =mT, m = constant. The solution of the modified gravity field equations has been generated by assuming that the deceleration parameter q is a function of the Hubble parameter H, i.e., q = bn/H (where b and n are constants, and n > 0), which yields the scale factor a = k[exp(nt) − 1]1/(1+b) (where k is a constant). The model exhibits deceleration at early times, and is currently accelerating. It is also seen that the model approaches isotropy at late times. Expressions for the Hubble parameter in terms of red-shift, luminosity distance, and state-finder parameter are derived and their significance is described in detail. The physical properties of the cosmological model are also discussed. An interesting feature of the model is that it has a dynamic cosmological parameter, which is large during the early universe, decreases with time, and approaches a constant at late times. This may help in solving the cosmological constant problem. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
445 KiB  
Proceeding Paper
Behavior of Various Scalar Field Potentials under Tracking Parameters of Quintessence Class of Scalar Field Models
by Tanisha Joshi
Phys. Sci. Forum 2021, 2(1), 39; https://doi.org/10.3390/ECU2021-09299 - 22 Feb 2021
Viewed by 1530
Abstract
Scalar field models are known for their dynamic nature, i.e., dynamic equations of state parameters to explain the late-time cosmic acceleration of the universe. The quintessence canonical scalar field with a potential is one such field which has been introduced to account for [...] Read more.
Scalar field models are known for their dynamic nature, i.e., dynamic equations of state parameters to explain the late-time cosmic acceleration of the universe. The quintessence canonical scalar field with a potential is one such field which has been introduced to account for the late time acceleration of the universe. In the present work, different kinds of scalar field potentials (under the quintessence cosmological model) are mathematically investigated using tracking parameters to examine whether these potentials show thawing or tracking behavior. Tracking parameters are considered because during cosmic evolution the dynamics of tracking depend on the variation of this particular parameter. Each potential is analyzed using this parameter and accordingly the behavior is shown. It is found that among the four potentials used, three show tracking properties and only one is shows the thawing property as per the tracking parameter. The tracking and thawing properties/behavior are discussed in the Results and Discussion sections of the paper. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
243 KiB  
Proceeding Paper
Balancing Asymmetric Dark Matter with Baryon Asymmetry by Sphaleron Transitions
by Arnab Chaudhuri and Maxim Khlopov
Phys. Sci. Forum 2021, 2(1), 41; https://doi.org/10.3390/ECU2021-09269 - 22 Feb 2021
Viewed by 1461
Abstract
The effect of the electroweak sphaleron transition in balance between baryon excess and and the excess of stable quarks of 4th generation is studied in this paper. Considering the non-violation of SU(2) symmetry and the conservation of electroweak and [...] Read more.
The effect of the electroweak sphaleron transition in balance between baryon excess and and the excess of stable quarks of 4th generation is studied in this paper. Considering the non-violation of SU(2) symmetry and the conservation of electroweak and new charges and quantum numbers of the new family, it makes possible sphaleron transitions between baryons, leptons and 4th family of leptons and quarks. In this paper, we have tried to established a possible definite relationship between the value and sign of the 4th family excess relative to baryon asymmetry. If U-type quarks are the lightest quarks of the 4th family and sphaleron transitions provide excessive U¯ antiquarks, asymmetric dark matter in the form of dark atom bound state of (U¯U¯U¯) with primordial He nuclei is balanced with baryon asymmetry. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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Proceeding Paper
On the Asymptotic Behavior of Neutrinos
by Giuseppe Gaetano Luciano
Phys. Sci. Forum 2021, 2(1), 44; https://doi.org/10.3390/ECU2021-09306 - 22 Feb 2021
Viewed by 1264
Abstract
Mixing transformations in QFT are non-trivial, since they are connected with the issue of the unitary inequivalence between Fock space for definite flavor fields and Fock space for definite mass fields. This poses the problem of selecting the right (i.e., physical) representation for [...] Read more.
Mixing transformations in QFT are non-trivial, since they are connected with the issue of the unitary inequivalence between Fock space for definite flavor fields and Fock space for definite mass fields. This poses the problem of selecting the right (i.e., physical) representation for asymptotic mixed fields. Here, we approach to the study of this inequivalence in the context of mixing of neutrinos. As a test-bench for our investigation, we consider the weak decay of a uniformly accelerated proton within the framework of the minimally extended SM. By relying on some core principles and predictions of the theory, such as the general covariance, the conservation of the family lepton numbers in the tree-level interaction vertices and the CP-symmetry violating effects in neutrino oscillations, we conclude that the only way to keep the formalism internally consistent is by resorting to the flavor representation. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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Proceeding Paper
Probing Inflation with Large-Scale Structure Data: The Contribution of Information at Small Scales
by Ivan Debono
Phys. Sci. Forum 2021, 2(1), 45; https://doi.org/10.3390/ECU2021-09371 - 1 Mar 2021
Viewed by 1618
Abstract
Upcoming full-sky large-scale structure surveys such as Euclid can probe the primordial Universe. Using the specifications for the Euclid survey, we estimate the constraints on the inflation potential beyond slow-roll. We use mock Euclid and Planck data from fiducial cosmological models using the [...] Read more.
Upcoming full-sky large-scale structure surveys such as Euclid can probe the primordial Universe. Using the specifications for the Euclid survey, we estimate the constraints on the inflation potential beyond slow-roll. We use mock Euclid and Planck data from fiducial cosmological models using the Wiggly Whipped Inflation (WWI) framework, which generates features in the primordial power spectrum. We include Euclid cosmic shear and galaxy clustering, with two setups (Conservative and Realistic) for the non-linear cut-off. We find that the addition of Euclid data gives an improvement in constraints in the WWI potential, with the Realistic setup providing marginal improvement over the Conservative for most models. This shows that Euclid may allow us to identify oscillations in the primordial spectrum present at intermediate to small scales. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>One-dimensional posteriors and marginalized contours (<math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics></math>) for the inflation parameters in the WWI: Featureless model. The addition of Euclid data results in a significant improvement in constraints for the amplitude parameter, and there is only slight improvement with Euclid Realistic compared to Euclid Conservative.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–A model. Improvement in the constraints is most evident in the amplitude parameter <math display="inline"><semantics> <msub> <mi>V</mi> <mn>0</mn> </msub> </semantics></math>. The constraints from Euclid Realistic are slightly better than Euclid Conservative.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–B model. There is significant improvement in constraints for all inflation parameters with the addition of Euclid data, but little difference between Euclid Conservative and Realistic.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–C model. As with WWW–A, there is some improvement when Euclid Realistic is used.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–D model. We note a significant improvement from Euclid Realistic over Euclid Conservative for all parameters.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWIP: Featureless model. Euclid Realistic shows some improvement over Euclid Conservative.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWIP: Planck-best-fit model. Again, Euclid Realistic shows some improvement over Euclid Conservative.</p>
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<p>One-dimensional posteriors and marginalized contours for the inflation parameters in the WWIP: Small-scale-feature model. We obtain closed contours for all the inflation parameters, with a significant improvement with Euclid data are added. Euclid Realistic provides further improvement.</p>
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Proceeding Paper
Coupling to Matter in Degenerate Scalar-Tensor Theories
by Sebastian Garcia-Saenz and Cédric Deffayet
Phys. Sci. Forum 2021, 2(1), 46; https://doi.org/10.3390/ECU2021-09309 - 22 Feb 2021
Viewed by 1253
Abstract
Scalar-tensor theories of gravity provide an intriguing and compelling approach to the dark energy problem. They have received increased attention in recent years thanks to a wealth of developments both in the theoretical and experimental sides. The class of models known as “degenerate” [...] Read more.
Scalar-tensor theories of gravity provide an intriguing and compelling approach to the dark energy problem. They have received increased attention in recent years thanks to a wealth of developments both in the theoretical and experimental sides. The class of models known as “degenerate” provide a particularly interesting proposal. These theories extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order, a virtue made possible by the existence of an additional constraint that removes the would-be instability associated to a ghost. This note presents a brief overview of the problem of matter coupling in degenerate scalar-tensor theories. It has been remarked that the presence of matter fields minimally coupled to the metric tensor can obstruct the degeneracy constraint, thus impairing the consistency of the theory. We explain through some illustrative examples the precise ways in which the extra degree of freedom may reappear. This occurs in the Hamiltonian language through a loss of constraints, which may happen either when the kinetic matrix is not block-diagonal in the presence of matter fields, or when the matter sector itself has constraints. We next turn to the more physically relevant case of fermionic matter, and show that spin-1/2 fermions evade these issues and can thus be consistently coupled to degenerate theories of scalar-tensor gravity. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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Proceeding Paper
Comparison between Three Paradigms of General Relativity
by Kareema Al Hosni and Mudhahir Al Ajmi
Phys. Sci. Forum 2021, 2(1), 48; https://doi.org/10.3390/ECU2021-09280 - 22 Feb 2021
Viewed by 1477
Abstract
Gravity formulated as a classical gauge theory is based on the Mach principle in terms of curvature scalar R by A. Einstein. The original idea of Einstein limits the gravity to act as a curvature in spacetime. However, there exist other possible classical [...] Read more.
Gravity formulated as a classical gauge theory is based on the Mach principle in terms of curvature scalar R by A. Einstein. The original idea of Einstein limits the gravity to act as a curvature in spacetime. However, there exist other possible classical fields such as torsion and non-metricity. The aim of this paper is to make a compatible comparison between three paradigms: Gravity as curvature via Einstein–Hilbert action, Teleparallel Gravity (TEGR) and Coincidence Gravity (CGR). In TEGR, a flat spacetime is considered as well as an asymmetric connection metric. In CGR, gravity is constructed in an equally flat, tortionless spacetime, which is ascribed to non-metricity. The strength and weakness of each formulation is tested in the framework of a homogeneous and isotropic cosmological background. Mainly, the equivalence between GR and TEGR is examined at the level of equation of motion. Furthermore, we study the interactions between dark energy, dark matter and radiation, and the stability of these models is explored. The implications of the interaction were tested in both early and late epochs of the universe. It has been found that mostly there is a similarity of description of the evolution of the universe provided by GR and TEGR, while CGR always showed different description. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Model I: Density parameters of dark energy, matter and radiation for GR, TEGR and CGR.</p>
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<p>Model I: Numerical solution for the system of density function versus redshift <span class="html-italic">z</span> for GR, TEGR and CGR.</p>
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<p>Model I: Dark energy, matter and radiation densities versus redshift <span class="html-italic">z</span> for GR, TEGR and CGR.</p>
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<p>Model II: Density parameters of dark energy, matter and radiation for GR, TEGR and CGR.</p>
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<p>Model II: Numerical solution for the system of density function versus redshift <span class="html-italic">z</span> for GR, TEGR and CGR.</p>
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<p>Model II: Dark energy, matter and radiation densities versus redshift <span class="html-italic">z</span> for GR, TEGR and CGR.</p>
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<p>Effective equation of state <math display="inline"><semantics> <msub> <mi>w</mi> <mrow> <mi>e</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> </semantics></math> versus redshift <span class="html-italic">z</span> for GR, TEGR and CGR.</p>
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1873 KiB  
Proceeding Paper
Earth’s Obliquity and Stellar Aberration Detected at the Clementine Gnomon (Rome, 1703)
by Costantino Sigismondi
Phys. Sci. Forum 2021, 2(1), 49; https://doi.org/10.3390/ECU2021-09323 - 22 Feb 2021
Viewed by 1697
Abstract
The Clementine Gnomon was built in 1700–1702 by the astronomer Francesco Bianchini, upon the will of Pope Clement XI. This meridian line is located in the Basilica of santa Maria degli Angeli e dei Martiri in Rome, and it is visited by thousands [...] Read more.
The Clementine Gnomon was built in 1700–1702 by the astronomer Francesco Bianchini, upon the will of Pope Clement XI. This meridian line is located in the Basilica of santa Maria degli Angeli e dei Martiri in Rome, and it is visited by thousands of students and tourists per year. This 45-m meridian line was designed to measure the secular variation of the obliquity of the ecliptic ε and to verify the tropical years’ length used in the Gregorian Calendar. With a pencil and a meter, a synchronized watch and a videocamera, we can obtain an accuracy of up to one arcsecond in the position of the solar center. The observations from 21 November 2020 to 19 January 2021 are analyzed to recover the solstice’s instant in Capricorn, the ingresses into Sagittarius and Aquarius, and the corresponding observational uncertainties. Astrometric corrections to the total length of the meridian line and to the pinhole’s height are found. The 5′11″ Eastward deviation of the meridian line between the two solstices, found by comparing our observations and the ephemerides, and the aberration of Sirius’ light explain the timing of the solstices and equinoxes calculated by Bianchini for 1703. The aberration in declination of Sirius explains the variations of its meridian position observed in 1702-3. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>The Celestial North Pole is elevated over the horizon of 41°54′30″, on the yellow marble tarsia. The vertical brass line is the boreal gnomon [<a href="#B1-psf-02-00049" class="html-bibr">1</a>,<a href="#B2-psf-02-00049" class="html-bibr">2</a>].</p>
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<p>Meridian observations of Sirius (in blue) by Francesco Bianchini at the Clementine Gnomon, also in daylight (from March to September) compared with the stellar aberration on declination calculated in the same dates (in red). The original table of observations published by Bianchini [<a href="#B1-psf-02-00049" class="html-bibr">1</a>] (p. 45) is reproduced on the left side with the original typeset.</p>
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<p>The southern limb of the Sun over 220 mark of the meridian line on 21 December 2020. The reddish penumbra is 5-mm thick, and the limb is darkened. On the right side, a paper meter with cm and mm marks is visible.</p>
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<p>Shifting of the effective pinhole along the meridian line (left North, right South), and the shadow’s effect of the cylinder.</p>
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<p>The image of the Sun entering the Aquarius tile on 19 January 2021.</p>
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349 KiB  
Proceeding Paper
New Black Hole Solutions in N=2 and N=8 Gauged Supergravity
by Antonio Gallerati
Phys. Sci. Forum 2021, 2(1), 50; https://doi.org/10.3390/ECU2021-09297 - 22 Feb 2021
Viewed by 1297
Abstract
We present a N=2 supergravity model that interpolates between all the single dilaton truncations of the gauged SO(8), N=8 supergravity. We provide new explicit non-extremal charged black hole solutions and their supersymmetric limits, exploiting the [...] Read more.
We present a N=2 supergravity model that interpolates between all the single dilaton truncations of the gauged SO(8), N=8 supergravity. We provide new explicit non-extremal charged black hole solutions and their supersymmetric limits, exploiting the non-trivial transformation of the Fayet–Iliopoulos parameters under electromagnetic duality to connect the electric and the magnetic configurations. We also provide the asymptotic charges, thermodynamics and boundary conditions of these black hole configurations. We then construct a new supersymmetric truncation of the maximal supergravity, with this new sector featuring non-extremal and supersymmetric black holes. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
501 KiB  
Proceeding Paper
Growth of Matter Perturbations in an Interacting Dark Energy Scenario Emerging from Metric-Scalar-Torsion Couplings
by Mohit Kumar Sharma and Sourav Sur
Phys. Sci. Forum 2021, 2(1), 51; https://doi.org/10.3390/ECU2021-09293 - 22 Feb 2021
Cited by 4 | Viewed by 2017
Abstract
We study the growth of linear matter density perturbations in a modified gravity approach of scalar field couplings with metric and torsion. In the equivalent scalar-tensor formulation, the matter fields in the Einstein frame interact as usual with an effective dark energy component, [...] Read more.
We study the growth of linear matter density perturbations in a modified gravity approach of scalar field couplings with metric and torsion. In the equivalent scalar-tensor formulation, the matter fields in the Einstein frame interact as usual with an effective dark energy component, whose dynamics are presumably governed by a scalar field that sources a torsion mode. As a consequence, the matter density ceases to be self-conserved, thereby making an impact not only on the background cosmological evolution but also on the perturbative spectrum of the local inhomogeneities. In order to estimate the effect on the growth of the linear matter perturbations, with the least possible alteration of the standard parametric form of the growth factor, we resort to a suitable Taylor expansion of the corresponding exponent, known as the growth index, about the value of the cosmic scale factor at the present epoch. In particular, we obtain an appropriate fitting formula for the growth index in terms of the coupling function and the matter density parameter. While the overall parametric formulation of the growth factor is found to fit well with the latest redshift-space-distortion (RSD) and the observational Hubble (OH) data at low redshifts, the fitting formula enables us to constrain the growth index to well within the concordant cosmological limits, thus ensuring the viability of the formalism. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Functional variations of (<b>a</b>) the growth factor <span class="html-italic">f</span>(<span class="html-italic">z</span>) and (<b>b</b>) the matter density contrast <math display="inline"><semantics> <mrow> <msup> <mi>δ</mi> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </semantics></math>(<span class="html-italic">z</span>), in the redshift range <span class="html-italic">z</span> ∈ [0,5], for the fiducial parametric settings <math display="inline"><semantics> <mrow> <msubsup> <mo>Ω</mo> <mn>0</mn> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math> (fixed) and <span class="html-italic">s</span> = 0, 0.01, and 0.02.</p>
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<p>Functional variations of the growth factor fitting error, <span class="html-italic">E<sub>f</sub></span>(<span class="html-italic">z</span>), in the redshift range <span class="html-italic">z</span> ∈ [0,2.5], for the fiducial parametric settings (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mo>Ω</mo> <mn>0</mn> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math> (fixed) and variable <span class="html-italic">s</span> ∈ [0,0.02]; (<b>b</b>) <span class="html-italic">s</span> = 0.01 (fixed) and variable <math display="inline"><semantics> <mrow> <msubsup> <mo>Ω</mo> <mn>0</mn> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> </mrow> </semantics></math> ∈ [0.24,0.32].</p>
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<p>2D posterior distribution (<math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math>-<math display="inline"><semantics> <mrow> <mn>3</mn> <mi>σ</mi> </mrow> </semantics></math> contour levels) for (<b>a</b>) the Gold dataset, and (<b>b</b>) its combination with the Hubble dataset. The solid blue lines denote the respective best-fits and dashed lines correspond to the respective <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> levels.</p>
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<p>2D posterior distribution (<math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math>-<math display="inline"><semantics> <mrow> <mn>3</mn> <mi>σ</mi> </mrow> </semantics></math> contour levels) for (<b>a</b>) the Gold dataset, and (<b>b</b>) its combination with the Hubble dataset. The solid blue lines denote the respective best-fits and dashed lines correspond to the respective <math display="inline"><semantics> <mrow> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> levels.</p>
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233 KiB  
Proceeding Paper
Testing General Relativity vs. Alternative Theories of Gravitation with the SaToR-G Experiment
by David Lucchesi, Luciano Anselmo, Massimo Bassan, Marco Lucente, Carmelo Magnafico, Carmen Pardini, Roberto Peron, Giuseppe Pucacco and Massimo Visco
Phys. Sci. Forum 2021, 2(1), 52; https://doi.org/10.3390/ECU2021-09274 - 22 Feb 2021
Viewed by 1485
Abstract
A new experiment in the field of gravitation, SaToR-G, is presented. The experiment aims to compare the predictions of different theories of gravitation in the limit of weak field and slow motion. The ultimate goal of the experiment is to look for possible [...] Read more.
A new experiment in the field of gravitation, SaToR-G, is presented. The experiment aims to compare the predictions of different theories of gravitation in the limit of weak field and slow motion. The ultimate goal of the experiment is to look for possible "new physics" beyond the current standard model of gravitation based on the predictions of general relativity. A key role in the above perspective is the theoretical and experimental framework within which to confine our work. To this end, we make our best efforts to exploit the framework suggested by Dicke over 50 years ago. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
264 KiB  
Proceeding Paper
De Sitter Solutions in Models with the Gauss-Bonnet Term
by Sergey Vernov and Ekaterina Pozdeeva
Phys. Sci. Forum 2021, 2(1), 53; https://doi.org/10.3390/ECU2021-09305 - 22 Feb 2021
Cited by 1 | Viewed by 1271
Abstract
De Sitter solutions play an important role in cosmology because the knowledge of unstable de Sitter solutions can be useful in describing inflation, whereas stable de Sitter solutions are often used in models of the late-time acceleration of the Universe. Einstein–Gauss–Bonnet models are [...] Read more.
De Sitter solutions play an important role in cosmology because the knowledge of unstable de Sitter solutions can be useful in describing inflation, whereas stable de Sitter solutions are often used in models of the late-time acceleration of the Universe. Einstein–Gauss–Bonnet models are actively used as both inflationary models and dark energy models. To modify the Einstein equations, one can add a nonlinear function of the Gauss–Bonnet term or a function of the scalar field multiplied on the Gauss–Bonnet term. The effective potential method essentially simplifies the search and stability analysis of de Sitter solutions, because the stable de Sitter solutions correspond to the minima of the effective potential. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
1695 KiB  
Proceeding Paper
Solar System Peculiar Motion from Mid Infra Red AGNs and Its Cosmological Implications
by Ashok K. Singal
Phys. Sci. Forum 2021, 2(1), 54; https://doi.org/10.3390/ECU2021-09270 - 22 Feb 2021
Cited by 2 | Viewed by 1498
Abstract
According to the Cosmological Principle, the Universe should appear isotropic, without any preferred directions, to a comoving observer. However, a peculiar motion of the observer, or equivalently of the solar system, might introduce a dipole anisotropy in some of the observed properties of [...] Read more.
According to the Cosmological Principle, the Universe should appear isotropic, without any preferred directions, to a comoving observer. However, a peculiar motion of the observer, or equivalently of the solar system, might introduce a dipole anisotropy in some of the observed properties of the Cosmos. The peculiar motion of the solar system, determined from the dipole anisotropy in the Cosmic Microwave Background Radiation (CMBR), gave a velocity 370 km/s along l = 264°, b = 48°. However, dipoles from number counts, sky brightness or redshift distributions in large samples of distant active galactic Nuclei (AGNs) have yielded values of the peculiar velocity many times larger than that from the CMBR, though in all cases the directions agreed with the CMBR dipole. Here we determine our peculiar motion from a sample of ~0.28 million AGNs, selected from the Mid Infra Red Active Galactic Nuclei (MIRAGN) sample comprising more than a million sources. We find a peculiar velocity more than four times the CMBR value, although the direction seems to be within ~2σ of the CMBR dipole. Since a real solar peculiar velocity should be the same whatever the data or the technique of observations may be, such discordant dipoles could imply that the explanation for the genesis of these dipoles, including that of the CMBR, might lie elsewhere. At the same time, a common direction for all these dipoles, determined from completely independent surveys by different groups, does indicate that these dipoles are not merely due to some systematics, and it might instead suggest a preferred direction in the Universe implying a genuine anisotropy, which would violate the Cosmological Principle, the core of modern cosmology. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>The sky distribution of ~0.28 million AGNs of our MIRAGN sample, plotted in equatorial coordinates. The sky position of the pole determined from our MIRAGN sample is indicated by M, along with the error ellipse, while other pole positions for various dipoles shown on the map are: N(NVSS), T(TGSS) and D(DR12Q). The CMBR pole at C has negligible errors.</p>
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<p>A plot of the integrated source counts N(&lt;W1) against W1, for our MIRAGN sample, showing the power law behaviour of the source counts.</p>
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332 KiB  
Proceeding Paper
On the Quantum Origin of a Dark Universe
by Saurya Das, Mohit Kumar Sharma and Sourav Sur
Phys. Sci. Forum 2021, 2(1), 55; https://doi.org/10.3390/ECU2021-09289 - 22 Feb 2021
Viewed by 1794
Abstract
It has been shown beyond reasonable doubt that the majority (about 95%) of the total energy budget of the universe is given by dark components, namely Dark Matter and Dark Energy. What constitutes these components remains to be satisfactorily understood however, despite a [...] Read more.
It has been shown beyond reasonable doubt that the majority (about 95%) of the total energy budget of the universe is given by dark components, namely Dark Matter and Dark Energy. What constitutes these components remains to be satisfactorily understood however, despite a number of promising candidates. An associated conundrum is that of the coincidence, i.e., the question as to why the Dark Matter and Dark Energy densities are of the same order of magnitude at the present epoch, after evolving over the entire expansion history of the universe. In an attempt to address these, we consider a quantum potential resulting from a quantum corrected Raychaudhuri–Friedmann equation in presence of a cosmic fluid, which is presumed to be a Bose–Einstein condensate (BEC) of ultralight bosons. For a suitable and physically motivated macroscopic ground state wave function of the BEC, we show that a unified picture of the cosmic dark sector can indeed emerge, thus resolving the issue of the coincidence. The effective Dark energy component turns out to be a cosmological constant, by virtue of a residual homogeneous term in the quantum potential. Furthermore, comparison with the observational data gives an estimate of the mass of the constituent bosons in the BEC, which is well within the bounds predicted from other considerations. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Enhancement of the BEC mass parameter <span class="html-italic">m</span>, relative to its Hubble value <math display="inline"><semantics> <msub> <mi>m</mi> <msub> <mrow/> <mi>H</mi> </msub> </msub> </semantics></math> (scaled by a factor of <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>), and the variation of the BEC density parameter at the present epoch, <math display="inline"><semantics> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <msub> <mrow/> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi mathvariant="italic">B</mi> <mo>)</mo> </mrow> </msubsup> </semantics></math>, with the decrease of the QB parameter <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math> from about <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mn>0.001</mn> </mrow> </semantics></math>. The <math display="inline"><semantics> <mi>ϵ</mi> </semantics></math>-axes ticks are in the log scale.</p>
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2275 KiB  
Proceeding Paper
Gravitoelectromagnetism: L’art Pour L’art—Or a Subject for the Classroom
by Friedrich Herrmann and Michael Pohlig
Phys. Sci. Forum 2021, 2(1), 56; https://doi.org/10.3390/ECU2021-09282 - 22 Feb 2021
Viewed by 2375
Abstract
At school and university, gravity is taught essentially in the Newtonian way. Newtonian mechanics originated at a time when there were no fields, when energy did not exist as a physical quantity, and when one still had to be satisfied with the concept [...] Read more.
At school and university, gravity is taught essentially in the Newtonian way. Newtonian mechanics originated at a time when there were no fields, when energy did not exist as a physical quantity, and when one still had to be satisfied with the concept of actions at a distance. A theory without such shortcomings, Maxwell’s electromagnetism, came into being about 150 years later. It could have served as a model for a modern theory of gravitation. In fact, such a theory of gravitation, gravitoelectromagnetism, was proposed by Heaviside. However, it did not establish itself, because, first, many effects it describes are very, very small; second, it makes certain statements that seem unacceptable to some researchers; and third, shortly thereafter, general relativity was born, which removed the old deficiencies and seemed to make a classical field theory of gravity superfluous. We argue that the subject of gravitoelectromagnetism is a legitimate one for teaching at school and university even now. On the one hand, general relativity is impractical for many applications because the mathematical effort is high, and on the other hand, the theory of gravitoelectromagnetism by no means describes only tiny effects. Rather, it solves a problem that is deliberately ignored in the traditional teaching of Newtonian mechanics: to which system do we assign the so-called potential energy? Where is the “potential” energy located? We also encounter some peculiarities of gravitoelectromagnetism that are caused by the fact that compressive and tensile stresses within the gravitational field are interchanged in comparison with the electromagnetic field. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>(<b>a</b>) The electric field pulls outward on the sphere; (<b>b</b>) with the charge kept constant, new field has been created. For this, energy had to be supplied to the system; (<b>c</b>) spring model: the mechanical stresses were discretized.</p>
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<p>(<b>a</b>) The gravitational field pushes on the sphere; (<b>b</b>) with the mass kept constant, new field has been created. For this, energy had to be removed from the system; (<b>c</b>) spring model: the mechanical stresses were discretized.</p>
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<p>The rod is moved upwards. In the process, energy flows within the rod from top to bottom. This energy gradually leaves the rod sideways.</p>
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<p>In the left part of the rope, the energy flows upward, in the right part downward. In the process, its current strength increases upwards in the left part and decreases downwards in the right part. The circuit is closed by the gravitational field in which the energy flows from the right to the left part of the rope.</p>
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<p>Energy flow corresponding to <a href="#psf-02-00056-f004" class="html-fig">Figure 4</a>, schematically.</p>
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<p>Horizontal section through the arrangement of <a href="#psf-02-00056-f004" class="html-fig">Figure 4</a>. The field lines of the <math display="inline"><semantics> <mstyle mathvariant="bold" mathsize="normal"> <mi>g</mi> </mstyle> </semantics></math> field point into the drawing plane. From the right to the left section of the rope, the energy flows through the gravitational field.</p>
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258 KiB  
Proceeding Paper
New Perspectives for Multifrequency GW Astronomy: Strong Gravitational Lensing of GW
by Aleksandra Piórkowska-Kurpas
Phys. Sci. Forum 2021, 2(1), 57; https://doi.org/10.3390/ECU2021-09272 - 22 Feb 2021
Viewed by 1235
Abstract
Direct detection of gravitational waves was for a long time the holy grail of observational astronomy. The situation changed in 2015 with the first registration of a gravitational wave signal (GW150914) by laboratory interferometers on Earth. Now, successful operating runs of LIGO/Virgo gravitational [...] Read more.
Direct detection of gravitational waves was for a long time the holy grail of observational astronomy. The situation changed in 2015 with the first registration of a gravitational wave signal (GW150914) by laboratory interferometers on Earth. Now, successful operating runs of LIGO/Virgo gravitational wave detectors, resulting in numerous observations of gravitational wave signals from coalescing double compact objects (mainly binary black hole mergers) with the first evidence of a coalescing binary neutron star system, has elevated multimessenger astronomy to an unprecedented stage. Double compact objects (binary black hole systems, mixed black hole–neutron star systems, and double neutron star systems) are the main targets of future ground-based and space-borne gravitational wave detectors, opening the possibility for multifrequency gravitational wave studies and yielding very rich statistics of such sources. This, in turn, makes it possible that certain, non-negligible amounts of double compact objects will have a chance of being strongly lensed. In this paper, we will discuss new perspectives for future detections of gravitational wave signals in the case of strong gravitational lensing. First, the expected rates of lensed gravitational wave signals will be presented. Multifrequency detections of lensed gravitational wave events will demand different treatments at different frequencies, i.e., wave approach vs. geometric optics approach. New possibilities emerging from such multifrequency detections will also be discussed. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
352 KiB  
Proceeding Paper
Reconstruction of Models with Variable Cosmological Parameter in f(R,T) Theory
by Rishi Kumar Tiwari, Aroonkumar Beesham and Bhupendra Kumar Shukla
Phys. Sci. Forum 2021, 2(1), 59; https://doi.org/10.3390/ECU2021-09372 - 1 Mar 2021
Cited by 1 | Viewed by 1450
Abstract
The standard ΛCDM model is reasonably successful in describing the universe, and is the most widely acceptable model in cosmology. However, there are several theoretical issues, such as the initial singularity, the cosmological constant problem, the particle nature of dark matter, the existence [...] Read more.
The standard ΛCDM model is reasonably successful in describing the universe, and is the most widely acceptable model in cosmology. However, there are several theoretical issues, such as the initial singularity, the cosmological constant problem, the particle nature of dark matter, the existence of anomalies in the cosmic microwave background radiation and on small scales, the predictions and tests of the inflationary scenario and whether general relativity is valid on the largest possible scales. Hence, there is growing interest in looking at modified theories. In this presentation, a reconstruction is made of the Friedmann–Lemaitre–Robertson–Walker models with a dynamic cosmological parameter in f(R,T) modified gravity. This theory has a number of pleasing features, such as the avoidance of the initial Big Bang singularity and a variable cosmological parameter. A dynamic cosmological parameter, which arises naturally in this theory, can solve the cosmological constant problem, and it is also a candidate for dark energy. In addition, a variable cosmological parameter fits observations better than the standard ΛCDM model. The model exhibits a transition from deceleration to acceleration. The time evolution of the physical parameters such as energy density, pressure and equation of state are analyzed. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>Deceleration parameter <span class="html-italic">q</span> against redshift <span class="html-italic">z</span>.</p>
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<p>Energy density against redshift <span class="html-italic">z</span>.</p>
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<p>Pressure against redshift <span class="html-italic">z</span>.</p>
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<p>Cosmological parameter against redshift <span class="html-italic">z</span>.</p>
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<p>EOS parameter against redshift <span class="html-italic">z</span>.</p>
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1964 KiB  
Proceeding Paper
On Spacetime Duality and Bounce Cosmology of a Dual Universe
by Mohammed B. Al-Fadhli
Phys. Sci. Forum 2021, 2(1), 61; https://doi.org/10.3390/ECU2021-09291 - 22 Feb 2021
Viewed by 2508
Abstract
The recent Planck Legacy 2018 release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model, which prefers a positively curved early [...] Read more.
The recent Planck Legacy 2018 release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model, which prefers a positively curved early Universe with a confidence level greater than 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the space-time worldlines are utilised to model the evolution of the Universe with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The worldlines reveal both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolved in opposite directions as distinct Universe sides during a first decelerating phase. The worldlines then indicate a second accelerated phase in reverse directions, whereby both sides free-fall towards each other under gravitational acceleration. The simulation of the predicted conformal curvature evolution demonstrates the fast orbital speed of the outer stars owing to external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the worldlines predict an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that the early Universe’s plasma could be separated and evolved into distinct sides of the Universe that collectively and geometrically inducing its evolution, physically explaining the effects attributed to dark energy and dark matter. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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<p>The hypersphere of a positively curved early Universe plasma expansion upon the CMB emissions. <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> </mrow> </semantics></math> is the reference radius of the intrinsic curvature and <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>p</mi> </msub> </mrow> </semantics></math> is the reference scale factor of the early Universe at the corresponding reference time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>p</mi> </msub> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>n</mi> <mo stretchy="false">^</mo> </mover> <mi>u</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>t</mi> <mo stretchy="false">→</mo> </mover> <mi>v</mi> </msub> </mrow> </semantics></math> are the normal and tangential vectors on the manifold boundary respectively regarding the extrinsic curvature.</p>
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<p>(<b>a</b>) Evolution of the wavefunction of matter/antimatter of one side of the Universe, and a radiation only wavefunction, in addition to the straight line of light cone (diagram is not to scale). (<b>b</b>) The evolution of Hubble parameter, <math display="inline"><semantics> <mi>H</mi> </semantics></math>, and its rate. The orange curves show a deceleration during the first <math display="inline"><semantics> <mrow> <mo>~</mo> <mn>10</mn> </mrow> </semantics></math> Gyr followed by an accelerated expansion rate.</p>
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<p>(<b>a</b>) A 2D schematic of the predicted cosmic topology of both sides at the first phase away from the early plasma, while the second phase corresponds to the reversal of the expansion direction. The future third phase corresponds to a spatial contraction, leading to a Big Crunch. (<b>b</b>) The apparent topology during the first and second phases caused by gravitational lensing effects.</p>
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<p>Schematic of the 3D spatial and 1D temporal dimensions of both sides, according to the wavefunction of space-time worldlines. (<b>a</b>) In the first phase, both sides expand away from the early plasma. (<b>b</b>) In the second stage, both sides expand in reverse directions and free-fall towards each other under gravitational acceleration. In the third phase, both sides contract leading to the big Crunch. Blue circles represent 3D slices of the Universe that are not necessarily simple path connected slices.</p>
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<p>The hypersphere of a compact core of a galaxy (the red-orange 4D hypersphere representing the local relativistic space-time of the cloud forming a galaxy) along its travel and spin through the conformal space-time (the blue-purple 4D independent background) of a pre-existing curvature that evolves over cosmic time.</p>
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<p>(<b>a</b>) External fields exerted on a galaxy as it travels through conformally curved space-time. Green curves represent the divergence in the conformal space-time curvature over cosmic time. Blue curves represent the simulated space-time continuum flux. (<b>b</b>) Simulation of a spiral galaxy rotation under external fields, where the blue represents the slowest tangential speeds, and red represents the fastest speeds.</p>
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740 KiB  
Proceeding Paper
Differentially Rotating Relativistic Stars beyond the J-Constant Law
by Panagiotis Iosif and Nikolaos Stergioulas
Phys. Sci. Forum 2021, 2(1), 62; https://doi.org/10.3390/ECU2021-09312 - 22 Feb 2021
Cited by 1 | Viewed by 1459
Abstract
The merger of a binary neutron star (BNS) system can lead to different final states depending on the total mass of the binary system and the equation of state (EOS). One of the possible outcomes of the merger is a long-lived (lifetime > [...] Read more.
The merger of a binary neutron star (BNS) system can lead to different final states depending on the total mass of the binary system and the equation of state (EOS). One of the possible outcomes of the merger is a long-lived (lifetime > 10 ms), compact and differentially rotating remnant. The Komatsu, Eriguchi and Hachisu (1989) differential rotation law (KEH) has been used almost exclusively in the literature to describe such configurations, despite the tension with corresponding rotational profiles reported from numerical simulations. New rotation laws suggested by Uryu et al. (2017) aspire to ease this tension and provide more realistic choices to describe the rotational profiles of BNS merger remnants. We recently started constructing equilibrium models with one of the new rotation laws proposed and comparing their physical properties to the KEH rotation law counterpart models. In addition, building on earlier work, the accuracy of the IWM-CFC conformal flatness approximation with the new differential rotation law was confirmed. Full article
(This article belongs to the Proceedings of The 1st Electronic Conference on Universe)
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Figure 1

Figure 1
<p>Angular velocity <math display="inline"><semantics> <mi mathvariant="sans-serif">Ω</mi> </semantics></math> profiles in the equatorial plane for model C6 (axis ratio <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>/</mo> <msub> <mi>r</mi> <mi>e</mi> </msub> </mrow> </semantics></math> = 0.43), constructed with the Uryu+ rotation law with <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mn>2.0</mn> <mo>,</mo> <mn>0.5</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> (see <a href="#sec3-psf-02-00062" class="html-sec">Section 3</a> for details). (<b>Left</b>) plotted versus the gravitationally redshifted angular momentum per unit rest mass and enthalpy <span class="html-italic">F</span>. (<b>Right</b>) plotted versus the coordinate radius <span class="html-italic">r</span>. Figure from [<a href="#B8-psf-02-00062" class="html-bibr">8</a>].</p>
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<p>Gravitational mass <span class="html-italic">M</span> versus the central energy density <math display="inline"><semantics> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> </semantics></math> for the definition of sequences A, B and C. For reference, the nonrotating (TOV) sequence (solid line), the mass-shedding (Kepler) limit for uniform rotation (dashed line) and the axisymmetric instability limit for uniform rotation (dotted line) are shown. Figure from [<a href="#B8-psf-02-00062" class="html-bibr">8</a>].</p>
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<p>Comparison of the gravitational mass <span class="html-italic">M</span> versus the circumferential radius <math display="inline"><semantics> <msub> <mi>R</mi> <mi>e</mi> </msub> </semantics></math> for the equilibrium models of sequences A (<b>Left</b>), B and C (<b>Right</b>), constructed with the Uryu+ and the KEH differential rotation laws. The values <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mn>2.0</mn> <mo>,</mo> <mn>0.5</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> were used for the Uryu+ law calculations. Figure from [<a href="#B8-psf-02-00062" class="html-bibr">8</a>].</p>
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<p>Effect of the different options for parameters <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> </semantics></math> for model B10 (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>/</mo> <msub> <mi>r</mi> <mi>e</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>). (<b>Left</b>) energy density profile <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </semantics></math> versus the coordinate radius <span class="html-italic">r</span> in the equatorial plane. (<b>Right</b>) angular velocity profile <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </semantics></math> in the equatorial plane. Figure from [<a href="#B8-psf-02-00062" class="html-bibr">8</a>].</p>
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<p>Gravitational mass <span class="html-italic">M</span> versus the circumferential radius <math display="inline"><semantics> <msub> <mi>R</mi> <mi>e</mi> </msub> </semantics></math> for the variations of sequence C, constructed with the Uryu+ differential rotation law and employing different <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> </semantics></math> values. Equilibrium models with <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mn>2.0</mn> <mo>,</mo> <mn>0.5</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1.5</mn> <mo>,</mo> <mn>0.5</mn> <mo>}</mo> </mrow> </semantics></math> are type C solutions, while models with <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mn>2.0</mn> <mo>,</mo> <mn>1.0</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1.5</mn> <mo>,</mo> <mn>1.0</mn> <mo>}</mo> </mrow> </semantics></math> are type A solutions [<a href="#B18-psf-02-00062" class="html-bibr">18</a>]. Figure from [<a href="#B8-psf-02-00062" class="html-bibr">8</a>].</p>
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<p>Comparison between full GR and the IWM-CFC approximation for model C5 (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>/</mo> <msub> <mi>r</mi> <mi>e</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>) calculated for the Uryu+ rotation law with <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>{</mo> <mn>2.0</mn> <mo>,</mo> <mn>0.5</mn> <mo>}</mo> </mrow> </mrow> </semantics></math>. (<b>Left</b>) energy density profile in the equatorial lane <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </semantics></math> versus the coordinate radius <span class="html-italic">r</span>. (<b>Right</b>) angular velocity profile in the equatorial plane <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Ω</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> </semantics></math> versus the coordinate radius <span class="html-italic">r</span>. Figure from [<a href="#B8-psf-02-00062" class="html-bibr">8</a>].</p>
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<p>Absolute values of the relative difference between full GR and IWM-CFC approximation for the gravitational mass <span class="html-italic">M</span>, the ratio of rotational to gravitational binding energy <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>/</mo> <mo>|</mo> <mi>W</mi> <mo>|</mo> </mrow> </semantics></math>, the equatorial circumferential radius <math display="inline"><semantics> <msub> <mi>R</mi> <mi>e</mi> </msub> </semantics></math> and the angular velocity at the center of the configuration <math display="inline"><semantics> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>c</mi> </msub> </semantics></math> for sequence C calculated with the KEH rotation law. Values at <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>/</mo> <mo>|</mo> <mi>W</mi> <mo>|</mo> <mo>∼</mo> <mn>0.16</mn> </mrow> </semantics></math> correspond to an axis ratio <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>p</mi> </msub> <mo>/</mo> <msub> <mi>r</mi> <mi>e</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>. Figure from [<a href="#B17-psf-02-00062" class="html-bibr">17</a>].</p>
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<p>Surfaces corresponding to empirical relations for the three different post-merger frequencies <math display="inline"><semantics> <msub> <mi>f</mi> <mi>peak</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>spiral</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mn>2</mn> <mo>−</mo> <mn>0</mn> </mrow> </msub> </semantics></math>, as a function of the chirp mass <math display="inline"><semantics> <msub> <mi>M</mi> <mi>chirp</mi> </msub> </semantics></math> and the equatorial circumferential radius <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mn>1.6</mn> </mrow> </msub> </semantics></math> of a nonrotating model with gravitational mass <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1.6</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math>. Figure from [<a href="#B21-psf-02-00062" class="html-bibr">21</a>].</p>
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