Linear growth of structure in massive gravity

TL;DR

This paper investigates the background evolution and matter perturbation growth in a specific massive gravity model, identifying conditions for stability and comparing its predictions to standard cosmology.

Contribution

It introduces a detailed analysis of scalar perturbation stability in extended quasidilaton massive gravity and explores the growth of structure under these conditions.

Findings

Stable perturbations occur with a specific scalar potential choice.

Growth of matter perturbations is scale-independent in the quasistatic limit.

Massive gravity predictions are compared to standard ΛCDM cosmology.

Abstract

We study background dynamics and the growth of matter perturbations in the extended quasidilaton setup of massive gravity. For the analysis of perturbations, we first choose a scalar field matter component and obtain the conditions under which all scalar perturbations are stable. We work in unitary gauge for the matter field, which allows us to directly map to known results in the limit of general relativity. By performing a parameter search, we find that the perturbations are unstable in general, while a particular choice of potential, where the scalar field effectively behaves like pressureless matter, allows for stable perturbations. We next consider the growth of matter perturbations in a cold dark matter-dominated Universe. Working in conformal Newtonian gauge, we obtain evolution equations for various observables including the growth factor and growth rate, and find scale-independent growth in the quasistatic and subhorizon approximations. We finally show how the Hubble parameter and matter perturbations evolve in massive gravity for a specific choice of parameter values, and how this evolution compares to the standard cosmological model consisting of a cosmological constant and cold dark matter.