Massive Gravity on Curved Background

TL;DR

This paper develops a covariant massive gravity theory on curved backgrounds by restoring symmetry with scalar fields, analyzing degrees of freedom on de Sitter space, and highlighting the theory's background-dependent nature.

Contribution

It introduces a method to construct generally covariant massive gravity theories on arbitrary curved backgrounds using scalar fields to restore symmetry.

Findings

The approach works for arbitrary curved backgrounds.

Explicit analysis confirms the physical degrees of freedom on de Sitter space.

Different backgrounds lead to different covariant massive gravity theories.

Abstract

We investigate generally covariant theories which admit a Fierz-Pauli mass term for metric perturbations around an arbitrary curved background. For this we restore the general covariance of the Fierz-Pauli mass term by introducing four scalar fields which preserve a certain internal symmetry in their configuration space. It is then apparent that for each given spacetime metric this construction corresponds to a completely different generally covariant massive gravity theory with different symmetries. The proposed approach is verified by explicit analysis of the physical degrees of freedom of massive graviton on de Sitter space.