The IR-completion of gravity: What happens at Hubble scales?

Abstract

We have recently proposed an 'ultra-strong' version of the equivalence principle (EP) that is not satisfied by standard semiclassical gravity. In the theory that we are conjecturing, the vacuum expectation value of the (bare) energy momentum tensor is exactly the same as in flat space: quartically divergent with the cut-off and with no spacetime-dependent (subleading) terms. The presence of such terms seems in fact related to some known difficulties, such as the black hole information loss and the cosmological constant problem. Since the terms that we want to get rid of are subleading in the highmomentum expansion, we attempt to explore the conjectured theory by 'infrared (IR)-completing' general relativity (GR). We consider a scalar field in a flat Friedman-Robertson-Walker (FRW) universe and isolate the first IR-correction to its Fourier modes operators that kills the quadratic (next to leading) timedependent divergence of the stress energy tensor vacuum expectation value (VEV). Analogously to other modifications of field operators that have been proposed in the literature (typically in the UV), the present approach seems to suggest a breakdown (here, in the IR, at large distances) of the metric manifold description. We show that corrections to GR are in fact very tiny, become effective at distances comparable to the inverse curvature and do not contain any adjustable parameter. Finally, we derive some cosmological implications. By studying the consistency of the canonical commutation relations, we infer a correction to the distance between two co-moving observers, which grows as the scale factor only when small compared to the Hubble length, but gets relevant corrections otherwise. The corrections to cosmological distance measures are also calculable and, for a spatially flat matter dominated Universe, go in the direction of an effective positive acceleration. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.