  We investigate the cosmological perturbations around FLRW solutions to non-
linear massive gravity with a new effective coupling to matter proposed
recently. Unlike the case with minimal matter coupling, all five degrees of
freedom in the gravity sector propagate on generic self-accelerating FLRW
backgrounds. We study the stability of the cosmological solutions and put
constraints on the parameters of the theory by demanding the correct sign for
the kinetic terms for scalar, vector and tensor perturbations.
