Isotropic singularities in shear-free perfect fluid cosmologies

TL;DR

This paper proves that shear-free, barotropic perfect fluid cosmologies with isotropic singularities are necessarily Friedmann–Robertson–Walker models, using two different methods to establish that the fluid flow must be geodesic.

Contribution

It demonstrates that under the shear-free condition, the only cosmologies with isotropic singularities are the well-known FRW models, extending previous results with new proof techniques.

Findings

Shear-free, barotropic, perfect fluid cosmologies with isotropic singularities are FRW models.

The fluid flow in these models must be geodesic.

The proof employs two different methods to establish the main result.

Abstract

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.