Classification of cosmological milestones

TL;DR

This paper analyzes the geodesic completeness of FLRW cosmological models using power expansions of the scale factor, revealing that some recent models are lightlike geodesically complete, unlike classical models.

Contribution

It introduces a method to assess geodesic completeness of cosmological models through generalized power expansions, highlighting the completeness of recent observationally supported models.

Findings

Classical models are timelike and lightlike geodesically incomplete.

Some recent models are lightlike geodesically complete.

Singularity strength varies according to Tipler and Krolak definitions.

Abstract

In this paper causal geodesic completeness of FLRW cosmological models is analysed in terms of generalised power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual definitions due to Tipler and Krolak. It is shown that while classical cosmological models are both timelike and lightlike geodesically incomplete, certain observationally alllowed models which have been proposed recently are lightlike geodesically complete.