Perturbations for massive gravity theories

Abstract

A theory of massive gravity depends on a nondynamical ``reference metric'' ${f}_{\ensuremath{\mu}\ensuremath{\nu}}$ which is often taken to be the flat Minkowski metric. In this paper we examine the theory of perturbations on a background with metric ${\overline{g}}_{\ensuremath{\mu}\ensuremath{\nu}}$ which does not coincide with the reference metric ${f}_{\ensuremath{\mu}\ensuremath{\nu}}$. 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 and show that it generically leads to instabilities.