Towards a physical interpretation for the Stephani Universes

TL;DR

This paper provides a physical interpretation for Stephani Universes, showing they can model realistic matter and gas conditions, and are observationally similar to standard cosmology in certain regimes.

Contribution

It offers a physical interpretation of Stephani Universes with realistic matter content and identifies conditions for regular, physically meaningful models.

Findings

Models satisfy ideal gas law and classical gas equations approximately.

Only positively curved slices avoid unphysical singularities.

In matter-dominated regimes, models are indistinguishable from standard FLRW cosmology.

Abstract

A physicaly reasonable interpretation is provided for the perfect fluid, sphericaly symmetric, conformally flat ``Stephani Universes''. The free parameters of this class of exact solutions are determined so that the ideal gas relation $p=n k T$ is identicaly fulfiled, while the full equation of state of a classical monatomic ideal gas and a matter-radiation mixture holds up to a good approximation in a near dust, matter dominated regime. Only the models having spacelike slices with positive curvature admit a regular evolution domain that avoids an unphysical singularity. In the matter dominated regime these models are dynamicaly and observationaly indistinguishable from ``standard'' FLRW cosmology with a dust source.