Viscous cosmology in the Kasner metric

Abstract

A Bianchi type-I metric of the Kasner form is used as input in Einstein's equations to explore which consequences thereby occur for the equation of state for the cosmic fluid. Both shear viscosity and bulk viscosity coefficients are assumed to be present. The solutions of Einstein's equations can naturally be categorized into two classes. Either the space becomes anisotropic, and the equation of state is determined once the Kasner parameters ${p}_{i}$ are given. Or the space becomes isotropic, and the equation of state emerges in the conventional form $p/\ensuremath{\rho}=\ensuremath{\gamma}\ensuremath{-}1$ with a definite value of \ensuremath{\gamma}. We also calculate the rate of entropy production $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\sigma}}$ per particle, and find that $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\sigma}}$ becomes as large as of order ${10}^{4}{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ if we go back to the very early universe, $t\ensuremath{\sim}{10}^{\ensuremath{-}4}\mathrm{s}.$ We also discuss the possibility of testing the anisotropy of the universe by means of redshift experiments.