Consistent long distance modification of gravity from inverse powers of the curvature

TL;DR

This paper explores long-distance modifications of gravity via inverse curvature powers, demonstrating models that are ghost-free, recover Einstein gravity locally, and could explain cosmic acceleration without dark energy.

Contribution

It introduces a class of inverse curvature gravity models that are ghost-free and can account for cosmic acceleration while remaining consistent with local gravity tests.

Findings

Models are ghost-free for specific curvature combinations.

Extra scalar field with Hubble-scale mass influences cosmic acceleration.

Modifications are negligible at Solar System scales but significant at galactic scales.

Abstract

In this paper we study long distance modifications of gravity obtained by considering actions that are singular in the limit of vanishing curvature. In particular, we showed in a previous publication that models that include inverse powers of curvature invariants that diverge for r->0 in the Schwarzschild geometry, recover an acceptable weak field limit at short distances from sources. We study then the linearisation of generic actions of the form L=F[R,P,Q] where P=R_{ab}R^{ab} and Q=R_{abcd}R^{abcd}. We show that for the case in which F[R,P,Q]=F[R,Q-4P], the theory is ghost free. Assuming this is the case, in the models that can explain the acceleration of the Universe without recourse to Dark Energy there is still an extra scalar field in the spectrum besides the massless spin two graviton. The mass of this extra excitation is of the order of the Hubble scale in vacuum. We nevertheless recover Einstein gravity at short distances because the mass of this scalar field depends on the background in such a way that it effectively decouples when one gets close to any source. Remarkably, for the values of the parameters necessary to explain the cosmic acceleration the induced modifications of gravity are suppressed at the Solar System level but can be important for systems like a galaxy.