Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes

Abstract

We consider the conformal Einstein equations for polytropic perfect fluid cosmologies which admit an isotropic singularity. For the polytropic index gamma strictly greater than 1 and less than or equal to 2 it is shown that the Cauchy problem for these equations is well-posed, that is to say that solutions exist, are unique and depend smoothly on the data, with data consisting of simply the 3-metric of the singularity. The analogous result for gamma=1 (dust) is obtained when Bianchi type symmetry is assumed.