Geodesic Behaviour around Cosmological Milestones

TL;DR

This paper classifies FLRW cosmological models based on the nature of their singularities using a generalized power expansion of the scale factor, providing a detailed understanding of their geodesic behavior near cosmological milestones.

Contribution

It introduces a comprehensive classification scheme for FLRW singularities using generalized Puiseux expansions, enhancing understanding of their geodesic properties.

Findings

Classified singularities as strong or weak based on power expansion analysis

Provided criteria for geodesic completeness near singularities

Enhanced understanding of cosmological model behaviors at milestones

Abstract

In this paper we provide a thorough classification of Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmological models in terms of the strong or weak character of their singularities according to the usual definitions. The classification refers to a generalised Puiseux power expansion of the scale factor of the model around a singular event.