General properties of cosmological models with an Isotropic Singularity

TL;DR

This paper explores the fundamental properties of cosmological models with an Isotropic Singularity, showing it is a point-like singularity and cannot occur in vacuum space-times, regardless of the matter source.

Contribution

It establishes general properties of models with an Isotropic Singularity independent of specific matter sources, expanding understanding beyond perfect fluid assumptions.

Findings

Isotropic Singularity is a point-like singularity.

Vacuum space-times cannot have an Isotropic Singularity.

Relationships with energy conditions and Hubble parameter are analyzed.

Abstract

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a $\gamma$-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.