Cosmological investigations of (extended) nonlinear massive gravity schemes with nonminimal coupling

In this paper we investigate the case of non-minimal coupling in the (extended) nonlinear massive gravity theories. We first consider massive gravity in the Brans-Dicke background such that the graviton mass is replaced by A[sup 2] ([sigma])m where [sigma] is the Brans-Dicke field and A([sigma]) is the conformal coupling and show that there is no viable thermal history of the Universe in this case. We then invoke a cubic Galileon term as the nonlinear completion of the [sigma] Lagrangian and show that there is a stable de Sitter solution in this case. As for the quasidilaton nonlinear massive gravity, the effective pressure of matter can be kept around zero by controlling the coupling constant, and the model is shown to be fit well with observations.