Singularities in FLRW Spacetimes

TL;DR

This paper argues that geodesic past-incompleteness in FLRW spacetimes does not necessarily indicate a true initial singularity, emphasizing the importance of physical viability of test particle trajectories in defining singularities.

Contribution

It introduces a criterion based on particle energy to distinguish physically meaningful geodesics, refining the understanding of singularities in FLRW cosmologies.

Findings

Only FLRW spacetimes with a vanishing scale factor at initial time are truly singular.

High-energy trajectories imply breakdown of particle description, challenging the link between geodesic incompleteness and singularities.

Non-physical trajectories can lead to false indications of initial singularities.

Abstract

We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.