Bianchi type I cosmological model with a viscous fluid

TL;DR

This paper investigates Bianchi I cosmological models with viscous fluids, deriving exact solutions and analyzing how shear and density evolve, showing consistency with classical models and matter creation from gravity.

Contribution

It introduces exact solutions for viscous Bianchi I models with a stiff fluid and explores their evolution, including matter creation and asymptotic behavior.

Findings

Models start with zero density and evolve by matter creation.

Solutions agree with Belinskii and Khalatnikov (1976) in asymptotic limits.

Models approach Friedmann universe at late times.

Abstract

Bianchi I cosmological models consisting of a fluid with both bulk and shear viscosity are studied. It is shown how the dynamical importance of the shear and the fluid density change in the course of evolution. Exact solutions with an equation of state $\rho = p$ for a stiff fluid are also obtained in several special cases, assuming the viscosity coefficients to be the power functions of the density. The results are, in some relevant cases, compared with those of Belinskii and Khalatnikov (1976) in the asymptotic limits and are seen to agree with them in that the models start with $\rho = 0$ at the beginning and evolve with the creation of matter by the gravitational field, finally approaching the Friedmann universe.