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Symmetry
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Physics and Mathematics of the Dark Universe
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Physics and Mathematics of the Dark Universe

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (1 June 2022) | Viewed by 14349

Special Issue Editors

Prof. Dr. Sergei V. Ketov

E-Mail Website
Guest Editor
1. Department of Physics, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami-ohsawa, Hachioji, Tokyo 192-0397, Japan
2. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa 277-8583, Japan
Dr. Yingqiu Gu

E-Mail Website
Guest Editor
School of Mathematical Science, Fudan University, Shanghai 200433, China

Special Issue Information

Dear Colleagues,

The evolution of the Universe is a fascinating topic in physics that attracts much attention. Despite remarkable progress in our understanding of the Universe during the last hundred years, there is overwhelming evidence for the existence of the Dark Universe that we do not understand. The Dark Universe includes (but is not limited to) dark energy, dark matter, cosmological inflation, and black holes. Gaining further insights demands new observational discoveries and advanced theoretical approaches in gravitational theory, quantum field theory with gravity, astroparticle physics, cosmology, and string theory, including the related mathematics. This Special Issue is devoted to current trends and new theoretical proposals in explaining the Dark Universe, including also gravity with extra dimensions, supersymmetric cosmology, string cosmology, AdS/CFT correspondence, primordial black holes and Swampland conjectures. Advanced theoretical physics and mathematics of the Dark Universe combine formal and phenomenological research and confront it to current observations, enhancing scientific knowledge about the Universe and connecting it to other branches of science.

Prof. Dr. Sergei V. Ketov
Dr. Yingqiu Gu
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • gravity
  • dark energy
  • dark matter
  • inflation
  • black holes
  • supergravity
  • string theory
  • extra dimensions

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Published Papers (7 papers)

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Research

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25 pages, 507 KiB  
Article
Dynamical Reason for a Cyclic Universe
by Ying-Qiu Gu
Symmetry 2021, 13(12), 2272; https://doi.org/10.3390/sym13122272 - 29 Nov 2021
Cited by 1 | Viewed by 2302
Abstract
By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by [...] Read more.
By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological model, we get the following results: (i) K=1, namely, the global spatial structure of the universe should be a three-dimensional sphere S3; (ii) 0≤Λ<10−24ly−2, the cosmological constant should be zero or an infinitesimal; (iii) a(t)>0, the initial singularity of the universe is unreachable, and the evolution of the universe should be cyclic in time. Since the matter components considered are quite complete and the proof is very elementary and strict, these conclusions are quite reliable in logic and compatible with all observational data. Obviously, these conclusions will be very helpful to correct some popular misconceptions and bring great convenience to further research other problems in cosmology such as the properties of dark matter and dark energy. In addition, the macroscopic Lagrangian of fluid model is derived. Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)
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16 pages, 730 KiB  
Article
Gravitational Decoupling in Higher Order Theories
by Joseph Sultana
Symmetry 2021, 13(9), 1598; https://doi.org/10.3390/sym13091598 - 31 Aug 2021
Cited by 22 | Viewed by 3082
Abstract
Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically [...] Read more.
Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM). Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)
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15 pages, 752 KiB  
Article
Bounce and Stability in the Early Cosmology with Anomaly-Induced Corrections
by Wagno Cesar e Silva and Ilya L. Shapiro
Symmetry 2021, 13(1), 50; https://doi.org/10.3390/sym13010050 - 30 Dec 2020
Cited by 9 | Viewed by 2099
Abstract
An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential e-folds could be very large, before the transition to the unstable version [...] Read more.
An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential e-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, we explore both stable expansion and the bounce solutions in the models with non-zero cosmological constant and the presence of background radiation. The critical part of the analysis concerns stability for small perturbations of the Hubble parameter. It is shown that the stability is possible for the variations in the bounce region, but not in the sufficiently distant past in the contraction phase. Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)
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16 pages, 314 KiB  
Article
S-Matrix and Anomaly of de Sitter
by Gia Dvali
Symmetry 2021, 13(1), 3; https://doi.org/10.3390/sym13010003 - 22 Dec 2020
Cited by 43 | Viewed by 2681
Abstract
S-matrix formulation of gravity excludes de Sitter vacua. In particular, this is organic to string theory. The S-matrix constraint is enforced by an anomalous quantum break-time proportional to the inverse values of gravitational and/or string couplings. Due to this, de Sitter [...] Read more.
S-matrix formulation of gravity excludes de Sitter vacua. In particular, this is organic to string theory. The S-matrix constraint is enforced by an anomalous quantum break-time proportional to the inverse values of gravitational and/or string couplings. Due to this, de Sitter can satisfy the conditions for a valid vacuum only at the expense of trivializing the graviton and closed-string S-matrices. At non-zero gravitational and string couplings, de Sitter is deformed by corpuscular 1/N effects, similarly to Witten–Veneziano mechanism in QCD with N colors. In this picture, an S-matrix formulation of Einstein gravity, such as string theory, nullifies an outstanding cosmological puzzle. We discuss possible observational signatures which are especially interesting in theories with a large number of particle species. Species can enhance the primordial quantum imprints to potentially observable level even if the standard inflaton fluctuations are negligible. Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)
16 pages, 1117 KiB  
Article
LISA Sensitivity to Gravitational Waves from Sound Waves
by Kai Schmitz
Symmetry 2020, 12(9), 1477; https://doi.org/10.3390/sym12091477 - 9 Sep 2020
Cited by 33 | Viewed by 4141
Abstract
Gravitational waves (GWs) produced by sound waves in the primordial plasma during a strong first-order phase transition in the early Universe are going to be a main target of the upcoming Laser Interferometer Space Antenna (LISA) experiment. In this short note, I draw [...] Read more.
Gravitational waves (GWs) produced by sound waves in the primordial plasma during a strong first-order phase transition in the early Universe are going to be a main target of the upcoming Laser Interferometer Space Antenna (LISA) experiment. In this short note, I draw a global picture of LISA’s expected sensitivity to this type of GW signal, based on the concept of peak-integrated sensitivity curves (PISCs) recently introduced in two previous papers. In particular, I use LISA’s PISC to perform a systematic comparison of several thousands of benchmark points in ten different particle physics models in a compact fashion. The presented analysis (i) retains the complete information on the optimal signal-to-noise ratio, (ii) allows for different power-law indices describing the spectral shape of the signal, (iii) accounts for galactic confusion noise from compact binaries, and (iv) exhibits the dependence of the expected sensitivity on the collected amount of data. An important outcome of this analysis is that, for the considered set of models, galactic confusion noise typically reduces the number of observable scenarios by roughly a factor of two, more or less independent of the observing time. The numerical results presented in this paper are also available in the online repository Zenodo. Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)
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16 pages, 290 KiB  
Article
Classical Variational Theory of the Cosmological Constant and Its Consistency with Quantum Prescription
by Claudio Cremaschini and Massimo Tessarotto
Symmetry 2020, 12(4), 633; https://doi.org/10.3390/sym12040633 - 16 Apr 2020
Cited by 9 | Viewed by 2673
Abstract
The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is provided. As a consequence, [...] Read more.
The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is provided. As a consequence, the cosmological constant is found to be identified with a Lagrange multiplier associated with the normalization constraint for the extremal metric tensor. In particular, it is proved that the same Lagrange multiplier identifies a 4-scalar gauge function generally dependent on an invariant proper-time parameter s. Such a result is shown to be consistent with the prediction of the cosmological constant based on the theory of manifestly-covariant quantum gravity. Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)

Review

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30 pages, 539 KiB  
Review
Cosmoparticle Physics of Dark Universe
by Maxim Khlopov
Symmetry 2022, 14(1), 112; https://doi.org/10.3390/sym14010112 - 9 Jan 2022
Cited by 5 | Viewed by 3157
Abstract
The physics of the dark Universe goes beyond the standard model (BSM) of fundamental interactions. The now-standard cosmology involves inflation, baryosynthesis and dark matter/energy corresponding to BSM physics. Cosmoparticle physics offers cross disciplinary study of the fundamental relationship of cosmology and particle physics [...] Read more.
The physics of the dark Universe goes beyond the standard model (BSM) of fundamental interactions. The now-standard cosmology involves inflation, baryosynthesis and dark matter/energy corresponding to BSM physics. Cosmoparticle physics offers cross disciplinary study of the fundamental relationship of cosmology and particle physics in the combination of its physical, astrophysical and cosmological signatures. Methods of cosmoparticle physics in studies of BSM physics in its relationship with inevitably nonstandard features of dark universe cosmology are discussed. In the context of these methods, such exotic phenomena as primordial black holes, antimatter stars in baryon asymmetrical Universe or multi-charged constituents of nuclear interacting atoms of composite dark matter play the role of sensitive probes for BSM models and their parameters. Full article
(This article belongs to the Special Issue Physics and Mathematics of the Dark Universe)
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