Conditions for defocusing around more general metrics in Infinite Derivative Gravity

TL;DR

This paper explores how Infinite Derivative Gravity can prevent singularities like the Big Bang and Hawking-Penrose by enabling defocusing of null rays, even with matter present, across various metrics including bouncing cosmologies.

Contribution

It extends the understanding of singularity avoidance in Infinite Derivative Gravity by analyzing defocusing conditions for general and specific cosmological metrics.

Findings

Infinite Derivative Gravity can avoid Big Bang singularity.

Defocusing of null rays is possible with matter included.

Conditions for defocusing are established for various FRW metrics.

Abstract

Infinite Derivative Gravity is able to resolve the Big Bang curvature singularity present in general relativity by using a simplifying ansatz. We show that it can also avoid the Hawking- Penrose singularity, by allowing defocusing of null rays through the Raychaudhuri equation. This occurs not only in the minimal case where we ignore the matter contribution, but also in the case where matter plays a key role. We investigate the conditions for defocusing for the general case where this ansatz applies and also for more specific metrics, including a general Friedmann-Robertson-Walker (FRW) metric and three specific choices of the scale factor which produce a bouncing FRW universe.