Massive gravity and structure formation

We study the growth of cosmological perturbations in the model of Lorentz-violating massive gravity. The Friedmann equation in this model acquires an unconventional term due to the Lorentz-breaking condensates which have the equation of state w=-1/(3γ) with γ being a free parameter taking values outside of the range [0,1/3]. Apart from the standard contributions, the perturbations above the Friedmann background contain an extra piece which is proportional to an arbitrary function ϑ(xⁱ) of the space coordinates. This function appears as an integration constant and corresponds to a nonpropagating scalar mode which may, however, become dynamical with the account of the higher-derivative corrections. For -1<γ<0 and γ=1 the anomalous perturbations grow slower than the standard ones and thus the model is compatible with observations. Whether the model is experimentally acceptable at other values of γ depends on the value of the function ϑ(xⁱ) at the beginning of the radiation-dominated epoch.