Cosmology and perturbations in massive gravity

TL;DR

This paper develops a formalism to analyze cosmological perturbations in the dRGT massive gravity theory, revealing that longitudinal modes are instantaneous at quadratic order but gain dynamics at cubic order.

Contribution

It introduces a general method for calculating perturbations around any cosmological background in massive gravity, including the full analysis for open FRW solutions.

Findings

Longitudinal modes are instantaneous at quadratic order.

Cubic interactions give the modes a time-kinetic term.

Formalism applies to arbitrary backgrounds.

Abstract

We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small scale limit, and for the open FRW solution we repeat the analysis around the full background. We find that the perturbations display similar properties: the longitudinal modes of the massive graviton are instantaneous at quadratic level, but they acquire a time-kinetic term at cubic order.