Viscous fluid cosmology

Abstract

In this paper we shall examine the effects of both bulk and shear viscosities upon a variety of cosmological models. We assume that the viscous terms can be modelled by dimensionless equations of state, and this allows us to write the Einstein equations as a system of autonomous differential equations. After briefly discussing the Friedmann--Robertson--Walker and Bianchi I models, we discuss in some detail the Bianchi V and Kantowski--Sachs models. In all cases we find the critical points of the flow and elucidate their nature, making use of the energy conditions. Because of our choice of dimensionless variables, (almost) all critial points represent self-similar solutions to the field equations. We also study the case of a Bianchi V perfect fluid model with a non-linear equation of state. We find that the models are structurally stable under the addition of shear viscosity, whereas they are structurally unstable under the introduction of bulk viscosity. Almost all of the Bianchi V models examined have initial singularities where the matter is dynamically unimportant; the Kantowski--Sachs models have final singularities where the matter is dynamically important.