Anisotropic Cosmological Models with Energy Density Dependent Bulk Viscosity

Abstract

An analysis is presented of the Bianchi type I cosmological models with a bulk viscosity when the universe is filled with the stiff fluid $p = ε$ while the viscosity is a power function of the energy density, such as $η= α|ε|^n$. Although the exact solutions are obtainable only when the $2n$ is an integer, the characteristics of evolution can be clarified for the models with arbitrary value of $n$. It is shown that, except for the $n = 0$ model that has solutions with infinite energy density at initial state, the anisotropic solutions that evolve to positive Hubble functions in the later stage will begin with Kasner-type curvature singularity and zero energy density at finite past for the $n> 1$ models, and with finite Hubble functions and finite negative energy density at infinite past for the $n < 1$ models. In the course of evolution, matters are created and the anisotropies of the universe are smoothed out. At the final stage, cosmologies are driven to infinite expansion state, de Sitter space-time, or Friedman universe asymptotically. However, the de Sitter space-time is the only attractor state for the $n <1/2 $ models. The solutions that are free of cosmological singularity for any finite proper time are singled out. The extension to the higher-dimensional models is also discussed.