  We study the physical propagating modes in a massive gravity model in curved
cosmological backgrounds, which we have found as classical solutions in our
previous paper. We show that, generically, there exist such the cosmological
background solutions consistent with the equations of motion where we assume
the ghost condensation ansatzes. Using the (1+3)-parametrization of the metric
fluctuations with 'unitary' gauge, we find that there is neither a scalar ghost
nor a tachyon in the spectrum of the propagating modes, the tensor modes become
massive owing to gravitational Higgs mechanism, and the model is free of the
Boulware-Deser instability. The price we have to pay is that the scalar sector
breaks the Lorentz-invariance, but there are no pathologies in the spectrum and
lead to interesting phenomenology. Moreover, we present a proof of the absence
of non-unitary modes for a specific ghost condensation model in a cosmological
background.
