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Generalised quadratic curvature, non-local infrared modifications of gravity and Newtonian potentials

Research output: Contribution to journalJournal articlepeer-review

Article number015024
<mark>Journal publication date</mark>11/12/2014
<mark>Journal</mark>Classical and Quantum Gravity
Issue number1
Number of pages23
Publication StatusPublished
Early online date19/06/14
<mark>Original language</mark>English


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.

Bibliographic note

20 pages, 2 figures. v2: some references and clarifications added