Weak Field Limit of Infinite Derivative Gravity

TL;DR

This paper investigates the weak field limit of infinite derivative gravity, demonstrating that it remains free of singularities at small scales and matches Einstein's gravity at large distances, with modified spin interactions.

Contribution

It provides the first calculation of scattering amplitudes and potential energies in infinite derivative gravity, revealing non-singular behavior and modifications to spin interactions at small scales.

Findings

Potential energy is non-singular as r approaches 0.

Spin-spin and spin-orbit interactions match Einstein's gravity at large distances.

Potential energy remains finite at small separations.

Abstract

A form of infinite derivative gravity is free from ghost-like instabilities with improved small scale behavior. In this theory, we calculate the tree-level scattering amplitude and the corresponding weak field potential energy between two localized covariantly conserved spinning point-like sources that also have velocities and orbital motion. We show that the spin-spin and spin-orbit interactions take the same form as in Einstein's gravity at large separations, whereas at small separations, the results are different. We find that not only the usual Newtonian potential energy but also the spin-spin and spin-orbit interaction terms in the potential energy are non-singular as one approaches r->0.