Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes

TL;DR

This paper investigates the mathematical properties of polytropic perfect fluid cosmologies with isotropic singularities, establishing well-posedness of the Einstein equations for certain polytropic indices and symmetry conditions.

Contribution

It proves the well-posedness of the conformal Einstein equations for polytropic fluids with specific indices, extending understanding of singularity behavior in cosmological models.

Findings

Solutions exist, are unique, and depend smoothly on initial data for gamma in (1,2].

Well-posedness is established for gamma=1 under Bianchi symmetry.

Results clarify the mathematical structure of isotropic singularities in cosmology.

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.