Nonlocal effective gravitational field equations and the running of Newton’s constant $G$

Nonperturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are proposed, which are intended to incorporate the gravitational, vacuum-polarization induced, running of Newton’s constant $G$. One attractive feature of this approach is that, from an underlying quantum gravity perspective, the resulting long-distance (or large time) effective gravitational action inherits only one adjustable parameter $\xi$, having the units of a length, arising from dimensional transmutation in the gravitational sector. Assuming the above scenario to be correct, some simple predictions for the long-distance corrections to the classical standard model Robertson-Walker metric are worked out in detail, with the results formulated as much as possible in a model-independent framework. It is found that the theory, even in the limit of vanishing renormalized cosmological constant, generally predicts an accelerated power-law expansion at later times $t\sim \xi \sim 1/H$.