Effects of the Shear Viscosity on the Character of Cosmological Evolution

TL;DR

This paper investigates how shear viscosity influences the evolution of Bianchi type I cosmological models, revealing conditions under which singularities are avoided and isotropization occurs, with implications for higher-dimensional theories.

Contribution

It provides exact equations for cosmological trajectories with shear viscosity as a power function of energy density, and demonstrates the absence of initial singularities for certain parameters.

Findings

No Einstein initial singularity for 0 ≤ n < 1.

Cosmologies start with zero energy density and evolve to isotropic Friedmann universe.

Dimensional reduction is possible even with shear-viscous matter.

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 $\zeta = \alpha \epsilon^n$. 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.