  We study cosmological perturbations of self-accelerating universe solutions
in the recently proposed nonlinear theory of massive gravity, with general
matter content. While the broken diffeomorphism invariance implies that there
generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the
gravity sector, we find that the scalar and vector degrees have vanishing
kinetic terms and nonzero mass terms. Depending on their nonlinear behavior,
this indicates either nondynamical nature of these degrees or strong couplings.
Assuming the former, we integrate out the 2 vector and 2 scalar degrees of
freedom. We then find that in the scalar and vector sectors, gauge-invariant
variables constructed from metric and matter perturbations have exactly the
same quadratic action as in general relativity. The difference from general
relativity arises only in the tensor sector, where the graviton mass modifies
the dispersion relation of gravitational waves, with a time-dependent effective
mass. This may lead to modification of stochastic gravitational wave spectrum.
