Massive gravity and structure formation

Abstract

We study the growth of cosmological perturbations in the model of Lorentz-violating massive gravity. The Friedman equation in this model acquires an unconventional term due to the Lorentz-breaking condensates which has 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 theta(x) of the space coordinates. This function appears as an integration constant and corresponds to a non-propagating 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 γdepends on the value of the function theta(x) at the beginning of the radiation-dominated epoch.