Cosmological Models with Two Fluids. I. Robertson?Walker Metric

Abstract

Exact solutions in terms of elementary functions are given for flat, homogeneous and isotropic, relativistic cosmological models which contain two fluids, each with an equation of state of the form $$ where p is the pressure, ? is the density, $$ is a constant, and $$ For other forms of v1/v2, the relevant solution is given in terms of a hypergeometric function. The cases when one of the v?s is equal to 2/3 or 2 are analogous to models with a Robertson?Walker metric with k = ± 1 and to anisotropic models of the type discussed by Jacobs respectively. All solutions for the two-fluid models can be written in terms of elementary functions when v1 = 0, which is analogous to a cosmological constant. The fact that all two-fluid solutions with v1 = 2/3 which can be written in terms of elementary functions are given means that all such one-fluid solutions with k = ± 1 are given.