Cosmic Acceleration and Growth of Structure in Massive Gravity

TL;DR

This paper explores a cosmological model within Generalised Massive Gravity, analyzing background evolution, linear perturbations, and gravitational wave propagation, revealing modifications to standard cosmology such as an effective fluid with w<-1 and massive tensor modes.

Contribution

It extends non-linear massive gravity by incorporating broken translation symmetry, demonstrating stable cosmological solutions and analyzing their implications for structure growth and gravitational waves.

Findings

Mass terms behave like a fluid with w<-1 at late times

Scalar graviton induces anisotropic stress affecting growth rate

Tensor modes acquire a time-dependent mass

Abstract

We introduce a cosmological model in the framework of Generalised Massive Gravity. This theory is an extension of non-linear massive gravity with a broken translation symmetry in the St\"uckelberg space. In a recent work, we showed the existence of cosmological solutions stable against linear perturbations. In the present paper, we build up on the previous result and study the evolution of the background solutions and the linear perturbations. At the background level, we find that the mass terms act like a fluid with time dependent equation of state $w < -1$ at late times. At linear order, we derive the Poisson's equation. We find that the scalar graviton mode invokes anisotropic stress, which brings a modification with respect to LCDM in the effective Newton's constant and the growth rate of matter perturbations. Moreover, we study the propagation of gravitational waves and find that the tensor modes acquire a time dependent mass.