New proposal for non-linear ghost-free massive F(R) gravity: Cosmic acceleration and Hamiltonian analysis

We propose new version of massive F(R) gravity which is natural generalization of convenient massive ghost-free gravity. Its Hamiltonian formulation in scalar-tensor frame is developed. We show that such F(R) theory is ghost-free. The cosmological evolution of such theory is investigated. Despite the strong Bianchi identity constraint the possibility of cosmic acceleration (especially, in the presence of cold dark matter) is established. Ghost-free massive F(R,T) gravity is also proposed.