Qualitative analysis of diagonal Bianchi type V imperfect fluid cosmological models

Abstract

The Einstein field equations for diagonal Bianchi type V imperfect fluid cosmological models with both viscosity and heat conduction are set up as an autonomous system of differential equations using dimensionless variables and a set of dimensionless equations of state. Models with and without a cosmological constant, λ, are investigated using the techniques from dynamical systems theory. It is shown that all models that satisfy the weak energy conditions isotropize. The introduction of viscosity (in particular) allows for a variety of different qualitative behaviors (including, for example, models with a negative deceleration parameter). Exact solutions that correspond to the singular points of the dynamical system are found. It is shown that the past asymptotic states are represented by self-similar cosmological models and, if λ=0, the future asymptotic states are also, in general, represented by self-similar cosmological models; in the exceptional cases the late time asymptotic state is represented by a de Sitter model with constant expansion, as is the case for solutions with λ ≠ 0.