Revealing Infinite Derivative Gravity's true potential: The weak-field limit around de Sitter backgrounds

TL;DR

This paper demonstrates that ghost-free Infinite Derivative Gravity (IDG) eliminates singularities in the gravitational potential around de Sitter backgrounds and aligns with General Relativity predictions at large distances, highlighting its potential to resolve classical singularities.

Contribution

The study shows that IDG produces a non-singular potential around de Sitter backgrounds and only a finite number of parameters influence its predictions, despite the theory's complexity.

Findings

IDG yields a non-singular potential around de Sitter backgrounds.

At large distances, IDG matches General Relativity predictions.

Differences between flat and de Sitter backgrounds are negligible below the Hubble scale.

Abstract

General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modelled as a de Sitter (dS) metric and we show that ghost-free Infinite Derivative Gravity (IDG) produces a non-singular potential around a dS background, while returning to the GR prediction at large distances. We also show that although there are an apparently infinite number of coefficients in the theory, only a finite number actually affect the predictions. By writing the linearised equations of motion in a simplified form, we find that at distances below the Hubble length scale, the difference between the IDG potential around a flat background and around a de Sitter background is negligible.