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 $w=-1/(3\gamma )$ with $\gamma$ 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 $\vartheta (x^i)$ 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 $-1<\gamma <0$ and $\gamma =1$ 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 $\gamma$ depends on the value of the function $\vartheta (x^i)$ at the beginning of the radiation-dominated epoch.