Massive gravity with non-minimal coupling

We propose new massive gravity theories with 5 dynamical degrees of freedom. We evade uniqueness theorems regarding the form of the kinetic and potential terms by adopting the "generalized massive gravity" framework, where a global translation invariance is broken. By exploiting the rotation symmetry in the field space, we determine two novel classes of theories. The first one is an extension of generalized massive gravity with a non-minimal coupling. On the other hand, the second theory produces a mass term that is different from de Rham, Gabadadze, Tolley construction and trivially has 5 degrees of freedom. Both theories allows for stable cosmological solutions without infinite strong coupling, which are free of ghost and gradient instabilities.