Perturbations for massive gravity theories

TL;DR

This paper investigates perturbations in massive gravity theories with a non-Minkowski reference metric, deriving the general mass term and analyzing specific cosmological cases, revealing deviations from the Fierz-Pauli form.

Contribution

It derives the general form of the perturbation mass term in massive gravity with arbitrary background metrics, extending previous Fierz-Pauli-based analyses.

Findings

Mass term generally deviates from Fierz-Pauli form on non-Minkowski backgrounds.

Explicit computation of the mass term in cosmological scenarios.

Highlights the importance of background choice in massive gravity perturbations.

Abstract

A theory of massive gravity depends on a non-dynamical 'reference metric' f_{\mu\nu} which is often taken to be the flat Minkowski metric. In this paper we examine the theory of perturbations on a background with metric g_{\mu\nu} which does not coincide with the reference metric f_{\mu\nu}. We derive the mass term for general perturbations on this background and show that it generically is not of the form of the Fierz-Pauli mass term. We explicitly compute it for some cosmological situations.