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

In this paper we show that there is a universal prediction for the Newtonian potential for a specific class of 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 nonsingular. We provide examples which can potentially test the scale of gravitational nonlocality up to 0.004 eV.