New symmetries in Fierz-Pauli massive gravity

TL;DR

This paper uncovers a new symmetry in Fierz-Pauli massive gravity that simplifies the linear perturbation spectrum to resemble that of General Relativity, with potential implications for gravitational theories.

Contribution

It introduces a novel symmetry in linear perturbations of Fierz-Pauli massive gravity with a cosmological constant, reducing degrees of freedom to GR-like modes.

Findings

The symmetry exists around flat background solutions with non-trivial Stuckelberg fields.

At linear order, only massless helicity 2 modes propagate.

The symmetry has potential implications for gravitational theory modifications.

Abstract

We expose a new symmetry for linear perturbations around a solution of non-linear Fierz-Pauli massive gravity plus a bare cosmological constant. The cosmological constant is chosen such that the background metric is flat while the Stuckelberg fields have a non-trivial profile. Around this background, at linear order the new symmetry reduces the propagating degrees of freedom to those of General Relativity, namely the massless helicity 2 modes only. We discuss the physical consequences and possible applications of these findings.