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

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 $Rf(R/\square )$ 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.

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

References in corpus (12)

• Degravitation of the Cosmological Constant and Graviton Width
• Black holes in an ultraviolet complete quantum gravity
• Dynamics of Nonlocal Cosmology
• Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity
• Reconstructing the Distortion Function for Nonlocal Cosmology
• Nonlocal Gravity Simulates Dark Matter
• Newtonian limit of nonlocal cosmology
• Nonlocal gravity and the diffusion equation
• Screening of cosmological constant in non-local gravity
• Diffusing non-local inflation: Solving the field equations as an initial value problem
• Newton's constant in f(R,R_{μν}R^{μν},\Box R) theories of gravity and constraints from BBN
• Reconstruction Procedure in Nonlocal Cosmological Models

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