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

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.