Massive gravity and structure formation

TL;DR

This paper investigates how Lorentz-violating massive gravity affects cosmological perturbation growth, revealing conditions under which the model aligns with observations and highlighting the role of an arbitrary function in perturbation behavior.

Contribution

It introduces a novel analysis of perturbations in Lorentz-violating massive gravity, emphasizing the impact of an arbitrary spatial function and parameter gamma on structure formation.

Findings

Perturbations grow slower for -1 < gamma < 0 and gamma = 1, consistent with observations.

The model's compatibility depends on the initial value of theta(x) during radiation era.

An extra non-propagating scalar mode may become dynamical with higher-derivative corrections.

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 \gamma depends on the value of the function theta(x) at the beginning of the radiation-dominated epoch.