Effects of the Shear Viscosity on the Character of Cosmological Evolution

Abstract

Bianchi type I cosmological models are studied that contain a stiff fluid with a shear viscosity that is a power function of the energy density, such as $ζ= αε^n$. These models are analyzed by describing the cosmological evolutions as the trajectories in the phase plane of Hubble functions. The simple and exact equations that determine these flows are obtained when $n$ is an integer. In particular, it is proved that there is no Einstein initial singularity in the models of $0\leq n < 1$. Cosmologies are found to begin with zero energy density and in the course of evolution the gravitational field will create matter. At the final stage, cosmologies are driven to the isotropic Fnedmann universe. It is also pointed out that although the anisotropy will always be smoothed out asymptotically, there are solutions that simultaneously possess non-positive and non-negative Hubble functions for all time. This means that the cosmological dimensional reduction can work even if the matter fluid having shear viscosity. These characteristics can also be found in any-dimensional models.