Exact analytical solution for an Israel–Stewart cosmology

Abstract

In this article we report a novel analytic solution describing a cosmological model with a matter content represented by a one dissipative fluid component, in the framework of the causal Israel–Stewart theory. The dissipative fluid is described by a barotropic equation of state $p= (\gamma -1) \rho$ and the bulk viscosity has been assumed of the form $\xi =\xi _{0}\rho ^{s}$. We study within the parameter space which label the solution, a suited region compatible with an accelerated expansion of the universe for late times, as well as stability properties of the solution at the critical parameter value $\gamma = 1$ and for $s = 1/2$. We study as well the consequences that arise from the positiveness of the entropy production along the time evolution. We found that the solution for pressureless dark matter, $\gamma = 1$, can well describe a universe with a transition from a decelerated expansion to an accelerated one at late times, but with a very large non-adiabatic contribution to speed of sound. Finally, the kinematics and thermodynamics properties of the solutions are discussed in terms of the type of expansion and entropy production.