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# Special Issue "Viscous Cosmology"

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

Deadline for manuscript submissions: 30 September 2020.

## Special Issue Editors

Prof. Dr. Marek Szydłowski
Website
Guest Editor
Department of High Energy Astrophysics, Jagiellonian University, Kraków, Poland
Interests: physics; cosmology; astronomy; philosophy of physics
Prof. Dr. Iver H. Brevik
Website
Co-Guest Editor
Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Interests: electrodynamics in continuous media; Casimir effect; cosmology; fluid dynamics
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## Special Issue Information

Dear Colleagues,

The Standard Cosmological Model is a strong idealization of the real Universe. It is assumed that spatial Universe is homogeneous and isotropic (with the Friedmann-Robertson-Walker symmetry) in which effects of dissipation are neglected at very beginning. One of the ways to question this idealization is to include effects of dissipation in the form of bulk viscosity.

Eckart (1940) introduced viscous contributions to the stress-energy tensor in his formulation of a relativistic theory of dissipative processes. At first this approach was used to avoid the initial singularity in the FRW cosmology. Nowadays, simple models of bulk viscosity, i.a., allow to study the effect of isotropic expansion on the thermodynamic properties of fluids and offer a phenomenological description of particle creation in the presence of strong gravitational fields.

Two main directions are looked upon here for a better understanding the role of viscosity in cosmology:

1. The search for a description of bulk viscosity to have a better insight in the context of general relativity and cosmology.
2. The study of cosmological models with dissipation effects where bulk viscosity is considered as a candidate for dark energy component of unsubstantial nature.

The purpose of the present Special Issue, entitled “Viscous Cosmology”, is the presentation of new ideas, methods of description of viscosity and its role in a cosmic evolution for better understanding of nature of dissipation in general relativity and cosmology.

Prof. Dr. Marek Szydłowski
Prof. Dr. Iver H. Brevik
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 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.

## Published Papers (3 papers)

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# Research

Open AccessArticle
Viscous Matter in FRW Cosmology
Symmetry 2020, 12(8), 1269; https://doi.org/10.3390/sym12081269 - 01 Aug 2020
Abstract
We investigate the dynamics of dust matter with bulk viscosity effects. We explored the analogy dynamical problem to Chaplygin gas. Due to this analogy we give exact solutions for the FRW cosmology with viscosity coefficient parameterized by the Belinskii–Khalatnikov power law dependence with [...] Read more.
We investigate the dynamics of dust matter with bulk viscosity effects. We explored the analogy dynamical problem to Chaplygin gas. Due to this analogy we give exact solutions for the FRW cosmology with viscosity coefficient parameterized by the Belinskii–Khalatnikov power law dependence with respect to energy density. These exact solutions are given in the form of hypergeometrical functions. We proved simple theorem which illustrated as viscosity effects can solved the initial singularity problem present in standard cosmological model. Full article
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Open AccessArticle
Remarks on Cosmological Bulk Viscosity in Different Epochs
Symmetry 2020, 12(7), 1085; https://doi.org/10.3390/sym12071085 - 01 Jul 2020
Abstract
The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is $ζ$ [...] Read more.
The intention of this paper is mainly two-fold. First, we point out a striking numerical agreement between the bulk viscosity in the lepton era calculated by Husdal (2016) and our own calculations of the present-day bulk viscosity when the functional form is $ζ ∼ ρ$ . From a phenomenological point of view, we thus seem to have an ansatz for the viscosity, which bridges the infancy of the Universe (∼1 s) with the present. This can also be looked upon as a kind of symmetry between the early-time cosmology and the present-day cosmology: it is quite remarkable that the kinetic theory-based bulk viscosity in the early universe and the experimentally-based bulk viscosity in the present universe can be covered by the same simple analytical formula. Second, we consider the Kasner universe as a typical anisotropic model of Bianchi-Type I, investigating whether this geometrical model is compatible with constant viscosity coefficients in the fluid. Perhaps surprisingly, the existence of a shear viscosity turns out to be incompatible with the Kasner model. By contrast, a bulk viscosity is non-problematic in the isotropic version of the model. In the special case of a Zel’dovich (stiff) fluid, the three equal exponents in the Kasner metric are even determined by the bulk viscosity alone, independent of the value of the fluid energy density. We also give a brief comparison with some other recent approaches to viscous cosmology. Full article
We investigate the particle creation, as well as the thermodynamics phenomenon of viscous generalized cosmic Chaplygin gas as a cosmic fluid by assuming the flat FRW universe. For this purpose, we extract various parameters such as the energy density $( ρ )$ , [...] Read more.
We investigate the particle creation, as well as the thermodynamics phenomenon of viscous generalized cosmic Chaplygin gas as a cosmic fluid by assuming the flat FRW universe. For this purpose, we extract various parameters such as the energy density $( ρ )$ , Hubble parameter $( H )$ , declaration parameter $( q )$ , temperature $( T f )$ , and particle number density $( n )$ in the presence of three different models of the particle creation rate ( $Γ$ ). We discuss the validity of the generalized second law of thermodynamics and thermal equilibrium condition under three models of $Γ$ and discuss the graphical behavior of above-mentioned terms. Full article