Exact Solutions in Modern Cosmology with Symmetry/Asymmetry

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

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 3421

Special Issue Editors


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Guest Editor
Department of Physics, Bauman Moscow State Technical University, Moscow, Russia
Interests: cosmology; theories of gravity; cosmological perturbations; gravitational waves

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Guest Editor
Department of Physics and Technical Disciplines, Ulyanovsk State Pedagogical University, Ulyanovsk, Russia
Interests: modified gravity; chiral self-gravitating models; exact solutions; inflation; dark energy; black holes; gravitational waves

Special Issue Information

Dear Colleagues,

Exact solutions are important for a correct understanding of the content of physical theories and the models built within the framework of physical theories. Fundamentals of the modern assumptions about the evolution of the universe and the origin of its large-scale structure were obtained on the basis of Friedmann's exact solutions of the Einstein equations, with the baryonic matter as the source of the gravitational field.

Within the framework of modern ideas about the evolution of the universe, various exotic matter fields and different modifications of Einstein's gravity theory are considered. The abundance of various models is associated with topical problems of modern cosmology, such as the problem of the cosmological constant, dark matter, dark energy, and some other problems. In this direction of research, the exact cosmological solutions can be considered criteria for the correctness of approximations, which are often used in the analysis of cosmological models.

The use of symmetries is one of the main methods of analysis in modern physical theories and their applications. Methods for constructing exact cosmological solutions include the use of the Noether point symmetry, Hojman symmetry, the use of nonlocal conservation laws, different form-invariant transformations, etc. Additionally, many other methods can be used to construct and analyze exact cosmological solutions.

The present Special Issue is devoted to the application of various methods for constructing exact solutions of cosmological dynamics equations to the analysis of actual models of the universe.

Prof. Dr. Igor Vladimirovich Fomin
Prof. Dr. Sergey Chervon
Guest Editors

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Keywords

  • cosmology
  • inflation
  • general relativity
  • modified gravity theories
  • scalar fields
  • exact solutions

Published Papers (4 papers)

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Research

13 pages, 285 KiB  
Article
Symmetry Transformations in Cosmological and Black Hole Analytical Solutions
by Edgar A. León and Andrés Sandoval-Rodríguez
Symmetry 2024, 16(4), 394; https://doi.org/10.3390/sym16040394 - 28 Mar 2024
Viewed by 681
Abstract
We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of [...] Read more.
We analyze the transformation of a very broad class of metrics that can be expressed in terms of static coordinates. Starting from a general ansatz, we obtain a relation for the parameters in which one can impose further symmetries or restrictions. One of the simplest restrictions leads to FLRW cases, while transforming from the initial static to other static-type coordinates can lead to near horizon coordinates, Wheeler–Regge, and isotropic coordinates, among others. As less restrictive cases, we show an indirect route for obtaining Kruskal–Szekeres within this approach, as well as Lemaître coordinates. We use Schwarzschild spacetime as a prototype for testing the procedure in individual cases. However, application to other spacetimes, such as de-Sitter, Reissner–Nordström, and Schwarzschild de Sitter, can be readily generalized. Full article
(This article belongs to the Special Issue Exact Solutions in Modern Cosmology with Symmetry/Asymmetry)
23 pages, 1412 KiB  
Article
Sustaining Quasi De-Sitter Inflation with Bulk Viscosity
by Sayantani Lahiri and Luciano Rezzolla
Symmetry 2024, 16(2), 194; https://doi.org/10.3390/sym16020194 - 06 Feb 2024
Cited by 2 | Viewed by 712
Abstract
The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which [...] Read more.
The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which H˙H2, with H(t) being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics, which takes into account non-equilibrium effects associated with bulk viscosity, which may have been present as the early universe underwent an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring introducing additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk viscosity pressure turns out to be time dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in the presence of bulk viscosity pressure. In addition, we construct a fluid description of inflation and demonstrate that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity-supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations, finding good agreement in most cases. Full article
(This article belongs to the Special Issue Exact Solutions in Modern Cosmology with Symmetry/Asymmetry)
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14 pages, 420 KiB  
Article
Exact (1 + 3 + 6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang–Mills Field, Gauss–Bonnet Term and Λ Term
by V. D. Ivashchuk, K. K. Ernazarov and A. A. Kobtsev
Symmetry 2023, 15(4), 783; https://doi.org/10.3390/sym15040783 - 23 Mar 2023
Viewed by 676
Abstract
We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and Λ term. We study so-called cosmological-type solutions defined on the product manifold M=R×R3×K, where K is 6d a Calabi–Yau manifold. [...] Read more.
We consider a 10-dimensional gravitational model with an SO(6)Yang–Mills field, Gauss–Bonnet term, and Λ term. We study so-called cosmological-type solutions defined on the product manifold M=R×R3×K, where K is 6d a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on K, we obtain exact cosmological solutions with exponential dependence of scale factors (upon t-variable) governed by two non-coinciding Hubble-like parameters: H>0 and h obeying H+2h0. We also present static analogs of these cosmological solutions (for H0, hH, and H+2h0). The islands of stability for both classes of solutions are outlined. Full article
(This article belongs to the Special Issue Exact Solutions in Modern Cosmology with Symmetry/Asymmetry)
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14 pages, 301 KiB  
Article
Classical and Quantum Cosmological Solutions in Teleparallel Dark Energy with Anisotropic Background Geometry
by Andronikos Paliathanasis
Symmetry 2022, 14(10), 1974; https://doi.org/10.3390/sym14101974 - 21 Sep 2022
Cited by 5 | Viewed by 701
Abstract
We investigate exact and analytic solutions for the field equations in the teleparallel dark energy model, where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like [...] Read more.
We investigate exact and analytic solutions for the field equations in the teleparallel dark energy model, where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exists for the description of the field equations, and variational symmetries are applied for the construction of invariant functions and conservation laws. The latter are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantum limit. Full article
(This article belongs to the Special Issue Exact Solutions in Modern Cosmology with Symmetry/Asymmetry)
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