Curvature perturbations of quasidilaton non-linear massive gravity

We study the cosmological perturbations of the recently proposed extension of non-linear massive gravity with a scalar field. The added scalar field ensures a new symmetry on the field space of the theory. The theory has the property of having a flat dS solution, in contrast to the standard dRGT massive gravity. The tensor part is the same as that of the standard dRGT and shows gravitational waves with a time dependent mass which modifies the dispersion relation. We obtain the curvature perturbation of the model on superhorizon scales for a specific choice of $\omega=0$ and find that the theory does not allow a constant curvature perturbation on the superhorizon scales and we have always a growing mode. The consistency of equations restricts the parameter space of the theory.