Can a Kasner universe with a viscous cosmological fluid be anisotropic?

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 the recent Comment of Cataldo and del Campo [Phys. Rev. D 61, 128301 (2000) ], on a previous work of the present authors [Phys. Rev. D $56,$ 3322 (1997)].