The Graviton Propagator in Asymptotically Safe Gravity with Non-Local Form Factors

Abstract

We analyze the flow of the background graviton propagator driven by the running of asymptotically safe form factors in four-dimensional quantum gravity at quadratic order in the curvature expansion. We construct the propagator in the $k=0$ limit and investigate its momentum dependence. The non-local form factors are then analytically continued to Minkowski spacetime, from which the corresponding Minkowskian propagator is obtained. We find a single pole at $q^2=0$ with positive residue and no additional ghost poles at this level of approximation. The corresponding Newtonian potential is found to be regular at $r=0$.