Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity

TL;DR

This paper demonstrates that ghost-free, infinite derivative gravity predicts a universal Newtonian potential that remains non-singular at short distances and matches the classical 1/r behavior at large scales, with potential experimental tests.

Contribution

It establishes a universal behavior of the Newtonian potential in ghost-free infinite derivative gravity and explores its testability at low energy scales.

Findings

Newtonian potential is 1/r at large distances

Potential becomes non-singular at short distances

Testable effects up to 0.004 eV scale

Abstract

In this paper we show that there is a universal prediction for the Newtonian potential for an infinite derivative, ghost-free, quadratic curvature gravity. We show that in order to make such a theory ghost-free at a perturbative level, the Newtonian potential always falls-off as 1/r in the infrared limit, while at short distances the potential becomes non-singular. We provide examples which can potentially test the scale of gravitational non-locality up to 0.004 eV.