TY - JOUR

T1 - Generalised quadratic curvature, non-local infrared modifications of gravity and Newtonian potentials

AU - Conroy, Aindriu

AU - Koivisto, Tomi

AU - Mazumdar, Anupam

AU - Teimouri, Ali

N1 - 20 pages, 2 figures. v2: some references and clarifications added

PY - 2014/12/11

Y1 - 2014/12/11

N2 - 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.

AB - 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.

KW - hep-th

KW - astro-ph.CO

KW - gr-qc

U2 - 10.1088/0264-9381/32/1/015024

DO - 10.1088/0264-9381/32/1/015024

M3 - Journal article

VL - 32

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 1

M1 - 015024

ER -