Cosmological perturbations of massive gravity coupled to DBI Galileons

TL;DR

This paper investigates the behavior of cosmological perturbations in a model combining massive gravity with Galileon scalar fields, analyzing stability conditions and the nature of propagating degrees of freedom.

Contribution

It provides a detailed analysis of the degrees of freedom and stability conditions in massive gravity coupled with Galileons around cosmological backgrounds.

Findings

Identification of ghost-free conditions

Conditions to avoid tachyonic instabilities

Vanishing kinetic terms for vector and scalar modes on self-accelerating solutions

Abstract

Certain scalar fields with higher derivative interactions and novel classical and quantum mechanical properties - the Galileons - can be naturally covariantized by coupling to nonlinear massive gravity in such a way that their symmetries and number of degrees of freedom are unchanged. We study the propagating degrees of freedom in these models around cosmologically interesting backgrounds. We identify the conditions necessary for such a theory to remain ghost free, and consider when tachyonic instabilities can be avoided. We show that on the self-accelerating branch of solutions, the kinetic terms for the vector and scalar modes of the massive graviton vanish, as in the case of pure massive gravity.