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.