Generalised Quadratic Curvature, Non-Local Infrared Modifications of Gravity and Newtonian Potentials

TL;DR

This paper explores non-local infrared modifications of gravity through quadratic curvature actions with inverse d'Alembertian operators, deriving field equations, analyzing weak-field limits, and proposing a new model that weakens gravity at large scales.

Contribution

It derives general field equations for non-local quadratic curvature gravity, analyzes their weak-field limit, and introduces a novel nonlocal model with potential implications for cosmological constant de-gravitation.

Findings

Newtonian potentials deviate from 1/r at large distances

Certain models do not introduce extra degrees of freedom in flat spacetime

A new exponential inverse d'Alembertian model exhibits infrared weakening of gravity

Abstract

Metric theories of gravity are studied, beginning with a general action that is quadratic in curvature and allows infinite inverse powers of the d'Alembertian operator, resulting in infrared non-local extensions of general relativity. The field equations are derived in full generality and their consistency is checked by verifying the Bianchi identities. The weak-field limit is computed and a straightforward algorithm is presented to infer the post-Newtonian corrections directly from the action. We then apply this to various infrared gravity models including non-local $Rf(R/ \Box)$ cosmology and non-local dark energy and massive gravity models. Generically the Newtonian potentials are not identical and deviate from the $1/r$ behaviour at large distances. However, the former does not occur in a specific class of theories that does not introduce additional degrees of freedom in flat spacetime. A new nonlocal model within this class is proposed, defined by the exponential of the inverse d'Alembertian. This model exhibits novel features, such as weakening of the gravity in the infrared, suggesting de-gravitation of the cosmological constant.