F(R)nonlinear massive theories of gravity and their cosmological implications

Abstract

We propose a nonlinear massive gravitational theory which includes F (R) modifications. This construction inherits the benefits of the de Rham-Gabadadze-Tolley model and is free of the Boulware-Deser ghost due to the existence of a Hamiltonian constraint accompanied by a nontrivial secondary one. The scalar perturbations in a cosmological background can be stabilized at the linear level for a wide class of the F (R) models. The linear scalar mode arisen from the F (R) sector can absorb the nonlinear longitudinal graviton, and hence, our scenario demonstrates the possibility of a gravitational Goldstone theorem. Finally, due to the combined contribution of the F (R) and graviton-mass sectors, the proposed theory allows for a large class of cosmological evolutions, such as the simultaneous and unified description of inflation and late-time acceleration.

F(R) nonlinear massive gravity and cosmology

“…8 for more details). For simplicity we work within the Einstein frame and expand the metrics using the famous Arnowitt-Deser-Misner (ADM) formalism:…”

“…6 We work in the Einstein frame, using the Lagrangian (6), and then consider perturbations around a homogeneous and isotropic background. 8 The scalar perturbations involve the metric…”

“…Inspired by the above discussion, we propose a modification of general relativity both in the UV and IR regimes, that is the F (R) nonlinear massive gravity. 8 The total theory is not only free of BD ghosts at the fundamental level, but it is also free of linear cosmological perturbative instabilities for the largest part of its parameter space, even in homogeneous and isotropic geometries. Finally, the increased freedom of both F (R) and massive-graviton sectors can lead to a huge class of interesting cosmological behaviors at early and late times, in agreement with observations.…”

Equivalent off-diagonal cosmological models and ekpyrotic scenarios in $$f(R)$$ f ( R ) -modified, massive, and einstein gravity

“…Another alternative came from the idea that the graviton may have a nontrivial mass as was proposed by Fierz and Pauli [1]. For recent reviews and related f (R) modifications and cosmological models, in general, with non-minimal coupling and dilaton-brane cosmology, local anisotropies and/or effective modeling of massive gravity, see, respectively, [6][7][8][9][10][11][12] and [13][14][15][16][17][18]. The modern version of a ghost-free (bimetric) massive gravity theory was made in a series of papers (recent reviews can be found in [19]): developing generic nonlinear versions of the FierzPauli theory, the so-called vDVZ discontinuity problem was solved via the Vainshtein mechanism [20][21][22] (avoiding the discontinuity by going beyond the linear theory).…”

Singular accelerated evolution in massiveF(R)bigravity

“…[8][9][10], it is possible to have a non-linear massive gravity, free of the Boulware-Deser ghost, at the decoupling limit [9] and in the full theory [10]. For some recent works on massive bigravity theories, see [11][12][13][14][15][16][17].…”