Spatially homogeneous and inhomogeneous cosmologies with equation of statep=?

Abstract

This paper gives an algorithm for generating solutions of the Einstein field equations which have an irrotational perfect fluid, with equation of statep=μ, as source, and which admit a two-parameter Abelian group of local isometries. The algorithm is used to derive a variety of new and known spatially homogeneous cosmological models, both tilted and nontilted. However, since the solutions in general only admit two Killing vectors, spatially inhomogeneous models are also obtained. Finally, it is pointed out that the solution generation technique used in this paper is closely related to solution generation techniques that have been used to generate solutions of the source-free Brans-Dicke field equations, and of the Einstein field equations with a massless scalar field as source.