Qualitative analysis of a class of inhomogeneous self-similar cosmological models

The authors 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 a plane autonomous system of ordinary differential equations which determines the spatial structure of the models. The properties of the models are analysed using the qualitative theory of plane autonomous systems. The models are of four distinct types, depending on their behaviour at large spatial distance. The matter-dominated models are either spatially periodic or asymptotically spatially homogeneous, and the vacuum-dominated models are either asymptotically spatially homogeneous or acceleration-dominated.