  The ghost-free theory of massive gravity with two dynamical metrics has been
shown to produce viable cosmological expansion, where the late-time
acceleration of the Universe is due to the finite range of the gravitational
interaction rather than a nonzero cosmological constant. Here the cosmological
perturbations are studied in this theory. The full perturbation equations are
presented in a general gauge and analyzed, focusing on subhorizon scales in the
quasistatic limit during the matter-dominated era. An evolution equation for
the matter inhomogeneities and the parameters quantifying the deviations from
general relativistic structure formation are expressed in terms of five
functions whose forms are determined directly by the coupling parameters in the
theory. The evolution equation has a similar structure to Horndeski-type
scalar-tensor theories, exhibiting a modified growth rate and scale-dependence
at intermediate wavenumbers. Predictions of the theory are confronted with
observational data on both background expansion and large-scale structure,
although care must be taken to ensure a model is stable. It is found that while
the stable models fit the data well, they feature deviations from the standard
cosmology that could be detected or ruled out by near-future experiments.
