Towards a Physical Interpretation for the Stephani Universes

A physically reasonable interpretation is provided for the perfect fluid, spherically symmetric, conformally flat "Stephani Universes". The free parameters of this class of exact solutions are determined so that the ideal gas relation p = nk_BT is identically fulfilled, 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 dynamically and observationally indistinguishable from "standard" FLRW cosmology with a dust source.