# Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity

## TL;DR

This paper explores how Infinite Derivative Gravity theories can produce non-singular, oscillating Newtonian potentials that allow for geodesic completeness, potentially resolving singularities in classical gravity.

## Contribution

It demonstrates that a broader class of IDG theories can yield non-singular potentials enabling null ray defocusing and geodesic completeness, extending previous results.

## Key findings

- Non-singular oscillating potentials match experimental data better than GR.
- IDG theories can be constructed to allow null ray defocusing.
- Conditions for geodesic completeness are compatible with non-singular potentials.

## Abstract

Recent study has shown that a non-singular oscillating potential, a feature of Infinite Derivative Gravity (IDG) theories, matches current experimental data better than the standard GR potential. In this work we show that this non-singular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays, and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past-complete, via the Raychaudhuri Equation, with the requirement of a non-singular Newtonian potential in an IDG theory. In so doing, we examine a class of Newtonian potentials characterised by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.