Generalized 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 arbitrary 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. This is then applied to various infrared gravity models including non-local Rf (R/ ) dark energy and non-local 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 non-local model within this class is proposed, defined by the exponential of the inverse d'Alembertian. This model exhibits novel features, such as the weakening of the gravity in the infrared, suggesting de-gravitation of the cosmological constant.

Conformal symmetry and nonlinear extensions of nonlocal gravity

“…(6) the "RR" model. Further work on the RR and RT models has been presented in [51][52][53][54][55][56][57][58][59].…”

Infrared Non-local Modifications of General Relativity

“…The other possibility for constructing transverse equations of motion, considered for instance in [65,75,96,104], is to start with a generally-covariant (formal) action. Indeed, say we have such an action for pure gravity…”

“…Therefore, gravity becomes unstable as soon asM 2 eff < 0. The Maggiore and Maggiore -Mancarella models, which correspond to the case ξ = 0, are currently receiving particular attention [71,76,78,104,119] because their phenomenology seems to privilege them among other non-local models that have been confronted with observations [65,68,70,73,74,97,107,109,110,[120][121][122][123][124]. Indeed, they have recently passed the constraints of a full Boltzmann/Monte Carlo Markov Chain analysis [78], of which they come out as statistically indistinguishable from ΛCDM, with respect to the current precision of the data.…”

Dynamical analysis ofR1□2Rcosmology: Impact of initial conditions and constraints from supernovae

“…The integral dependence of the corrections could generate the observed acceleration at the present cosmological epoch dynamically and without special fine-tunings. However, detailed investigations have shown that, although the function f can be chosen in such a way that the background expansion is consistent with the data [21][22][23] and the model has a viable Newtonian limit [24,25], the impact of the nonlocal corrections on the evolution of perturbations is strong and utterly rules the model out when this is confronted with large-scale structure data [26]. On top of that, nonlocal modifications of gravity result generically in instabilities at the level of perturbations, at least if they involve tensorial terms such as (W µνρσ / 2 )W µνρσ [27] with W µνρσ the Weyl tensor appearing in models inspired by the conformal anomaly [28,29].…”