Exact Solutions in Multidimensional Cosmology with Shear and Bulk Viscosity

TL;DR

This paper derives exact Kasner-like solutions for a multidimensional cosmological model with shear and bulk viscosity, analyzing their implications for universe evolution, compactification, and entropy production.

Contribution

It presents new exact solutions in multidimensional viscous cosmology, including a non-singular isotropic case, and explores their physical implications.

Findings

Exact Kasner-like solutions derived

Non-singular isotropic viscous solution identified

Insights into dynamical compactification and entropy production

Abstract

Multidimensional cosmological model describing the evolution of a fluid with shear and bulk viscosity in $n$ Ricci-flat spaces is investigated. The barotropic equation of state for the density and the pressure in each space is assumed. The second equation of state is chosen in the form when the bulk and the shear viscosity coefficients are inversely proportional to the volume of the Universe. The integrability of Einstein equations reads as a colinearity constraint between vectors which are related to constant parameters in the first and second equations of state. We give exact solutions in a Kasner-like form. The processes of dynamical compactification and the entropy production are discussed. The non-singular $D$-dimensional isotropic viscous solution is singled out.