## 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 formore »