Dynamical equilibrium states of the orthogonally transitive cosmologies: a class of inhomogeneous self-similar cosmological models

Abstract

We consider a class of spatially inhomogeneous cosmological models in which the fluid flow is tangential to the orbits of a three-parameter similarity group. The temporal evolution of the models is determined by the similarity group, and the Einstein field equations reduce to an autonomous system of ordinary differential equations which determines the spatial structure of the models. The theory of dynamical systems is then used to give a qualitative description of this spatial structure. Generically the models are vacuum-dominated and acceleration-dominated at large spatial distances. There exists an atypical subclass of models which is matter-dominated and asymptotically spatially homogeneous at large spatial distances. It has been conjectured previously that these models act as asymptotic states, for less symmetric cosmological models, at late times.