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Cosmology in rotation-invariant massive gravity with non-trivial fiducial metric

We investigate the cosmology of SO(3)-invariant massive gravity with 5 degrees of freedom. In contrast with previous studies, we allow for a non-trivial fiducial metric, which can be justified by invoking, for example, a dilaton-like global symmetry. We write the homogeneous and isotropic equations of motion in this more general setup and identify, in particular, de Sitter solutions. We then study the linear perturbations around the homogeneous cosmological solutions, by deriving the quadratic Lagrangian governing the dynamics of scalar, vector and tensor modes. We thus obtain the conditions for the perturbations to be well-behaved. We show that it is possible to find de Sitter solutions whose perturbations are weakly coupled and stable, i.e. without ghost-like or gradient instabilities.