Conformal symmetry and nonlinear extensions of nonlocal gravity

Abstract

We study two nonlinear extensions of the nonlocal R□ −2 R gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing □ −2 with ð−□ þ R=6Þ −2 , which is the operator that enters the action for a conformally-coupled scalar field, or replacing □ −2 with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today w DE ≃ −1.01, which very closely mimics ΛCDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordial universe and accelerated expansion in the recent epoch.

Gravity in the infrared and effective nonlocal models

“…This is the operator that enters in the conformal anomaly in four dimensions and, from the point of view of conformal invariance, is the natural generalization of the d'Alembertian from two to four dimensions. This model had a viable cosmological evolution [240], although its prediction for the equation of state of DE, w 0 −1.31, already seemed off with respect to the observations, as was indeed confirmed from a MCMC analysis in [23]. In any case, what definitely ruled out the model was the realization that, in the tensor sector, it predicts a speed of GWs different from the speed of light [23].…”

Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory †

“…These are nonlocal gravitational interactions dictating the behaviour of gravitational interactions at large cosmological scales. It can be understood as a heuristic derivation of the non-local action that has been studied extensively in [11,12,14] and is seen to agree with the various cosmological data as good as Λ-CDM. Defining the induced Newton's constant as 9/(32πG) −1 = ξ 1 κ 2 , and pulling out the factor of Planck's mass from the action allows to make comparison with the existing models in [11,12,14].…”

“…It is reasonably well understood that a slowly rolling scalar give rise to negative pressure generating dark energy effects, which is the case in quintessence model [3][4][5][6] and k-essence model [7][8][9]. Beside the existence of other possibilities, an interesting proposal involving non-locality has been proposed recently [10][11][12], where it was noticed that a particular kind of non-locality generates late-time accelerated expansion in the Universe fitting the darkenergy data as well as Λ-CDM [13,14]. However, a fundamental local explanation for it is currently lacking.…”

“…The scale-invariant higher-derivative induced gravity model coupled with scalars, undergoes symmetry breaking via quantum corrections [18], thereby inducing mass for the scalar leading to its decoupling [19,20]. In a model comprising of more than one scalar, if one of the scalar gets decoupled, a phase of accelerated expansion is achieved at late times arising due to the generation of non-locality following the integration of residual scalars [11,12,14].…”

On Nonlocal Modified Gravity and Its Cosmological Solutions

“…Perturbations and physical excitations of the equations of motion of action (24) around the de Sitter background are considered in [34] and [35], respectively. As some recent developments in nonlocal modified gravity, see [44,21,25,41,53,68].…”