Can a Kasner Universe with a Viscous Cosmological Fluid be Anisotropic?

TL;DR

This paper investigates the effects of viscosity on the anisotropy of Kasner universes, finding that viscous fluids enforce isotropy, contrasting with ideal fluids which allow anisotropic Kasner solutions.

Contribution

It demonstrates that viscous cosmological fluids prevent anisotropic Kasner metrics, providing explicit relations between fluid properties and the isotropic Kasner metric.

Findings

Viscous fluids lead to isotropic Kasner universes.

Explicit formulas relate fluid density, pressure, and viscosity to the Kasner metric.

Viscosity enforces isotropy in Kasner cosmologies.

Abstract

A Bianchi type -I metric of Kasner form is considered, when the space is filled with a viscous fluid. Whereas an ideal (nonviscous) fluid permits the Kasner metric to be anisotropic provided that the fluid satisfies the Zel'dovich equation of state, the viscous fluid does not permit the Kasner metric to be anisotropic at all. In the latter case, we calculate the Kasner (isotropic) metric expressed by the fluid's density, pressure, and bulk viscosity, at some chosen instant $t=t_0$. The equation of state is also calculated. The present paper is related to a recent Comment of Cataldo and del Campo [Phys. Rev. D, scheduled to April 15, 2000], on a previous work of the present authors [Phys. Rev. D {\bf 56}, 3322 (1997)].