On Past Singularities in $k=0$ FLRW Cosmologies

TL;DR

This paper demonstrates that spatially flat FLRW cosmologies with barotropic matter obeying only the weak energy condition and a nonnegative cosmological constant still contain a past singularity, extending previous singularity theorems.

Contribution

It extends the singularity theorem to include models with only the weak energy condition and a nonnegative cosmological constant using topological dynamical systems methods.

Findings

Past singularities exist under weaker energy conditions.

Topological methods effectively analyze singularities in cosmological models.

Results applicable to broader classes of cosmological models.

Abstract

The fundamental singularity theorem of FLRW cosmologies assumes that the matter content in the cosmological model obeys the strong energy condition along with a nonpositive cosmological constant which gives rise to an irrotational geodesic singularity. In this paper, we show that the important case of a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe with barotropic matter obeying only the \emph{weak} energy condition with a nonnegative cosmological constant also contains a past singularity. We accomplish this using topological methods from dynamical systems theory. The methods employed in this paper are sufficiently general that they could be extended to other models to study the existence of past singularities.