Nonlocal Effective Gravitational Field Equations and the Running of Newton's G

TL;DR

This paper proposes covariant effective field equations incorporating a quantum gravity motivated running of Newton's G, predicting late-time accelerated expansion in cosmology with a single adjustable parameter.

Contribution

It introduces a covariant framework for the gravitational field equations that include quantum-induced running of G, with a minimal parameter and applications to cosmological models.

Findings

Predicts a slow increase of G with distance from quantum effects.

Results suggest an accelerated power-law expansion at late times.

Framework is model-independent and rooted in quantum gravity insights.

Abstract

Non-perturbative 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 $t \sim \xi \sim 1/H$.