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

TL;DR

This paper introduces a nonlinear massive gravity theory incorporating $F(R)$ modifications, which is free of ghosts and can explain various cosmological phenomena including inflation and late-time acceleration.

Contribution

It develops a ghost-free $F(R)$ nonlinear massive gravity model that stabilizes scalar perturbations and unifies early and late universe acceleration.

Findings

Scalar perturbations can be stabilized at linear level.

The model absorbs nonlinear longitudinal gravitons.

Allows for diverse cosmological evolutions including inflation and acceleration.

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.