Cosmology of F(R) nonlinear massive gravity

The theory of nonlinear massive gravity can be extended into the F(R) form as developed by Cai et al. [Phys. Rev. D 90, 064051 (2014)]. Being free of the Boulware-Deser ghost, such a construction has the additional advantage of exhibiting no linear instabilities around a cosmological background. We investigate various cosmological evolutions of a universe governed by this generalized massive gravitational theory. Specifically, under the Starobinsky Ansatz, this model provides a unified description of the cosmological history, from early-time inflation to late-time self-acceleration. Moreover, under viable F(R) forms, the scenario leads to a very interesting dark energy phenomenology, including the realization of the quintom scenario without any pathology. Finally, we provide a detailed analysis of the cosmological perturbations at linear order, as well as the Hamiltonian constraint analysis, in order to examine the physical degrees of freedom.