Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds

TL;DR

This paper establishes conditions under which infinite derivative gravity can prevent cosmological singularities by causing null rays to defocus, contrasting with general relativity, and extends the analysis to more complex backgrounds.

Contribution

It derives criteria for defocusing of null rays in infinite derivative gravity and demonstrates how this can avoid singularities around expanding backgrounds.

Findings

Null rays can defocus in infinite derivative gravity, preventing singularities.

Conditions for defocusing are derived for (A)dS and (A)dS-Bianchi I backgrounds.

Explicit examples show defocusing is achievable under certain perturbations.

Abstract

We derive the conditions whereby null rays `defocus' within Infinite Derivative Gravity for perturbations around an (A)dS background, and show that it is therefore possible to avoid singularities within this framework. This is in contrast to Einstein's theory of General Relativity. We further extend this to an (A)dS-Bianchi I background metric, and also give an example of a specific perturbation where defocusing is possible given certain conditions.