Evolution of a universe filled with a causal viscous fluid

Abstract

The behaviour of solutions to the Einstein equations with a causal viscous fluid source is investigated. In this model we consider a spatially flat Robertson-Walker metric, the bulk viscosity coefficient is related to the energy density as $\zeta = \alpha \rho^{m}$, and the relaxation time is given by $\zeta/\rho$. In the case $m = 1/2$ we find the exact solutions and we verify whether they satisfy the energy conditions. Besides, we study analytically the asymptotic stability of several families of solutions for arbitrary $m$. We find that the qualitative asymptotic behaviour in the far future is not altered by relaxation processes, but they change the behaviour in the past, introducing singular instead of deflationary evolutions or making the Universe bounce due to the violation of the energy conditions.