Superluminality in the Fierz--Pauli massive gravity

TL;DR

This paper investigates the propagation of helicity-1 gravitons in Fierz--Pauli massive gravity, revealing that superluminal propagation can occur within the effective theory's validity range, raising concerns for modifications of General Relativity.

Contribution

It demonstrates that superluminal propagation of helicity-1 gravitons is generic in Fierz--Pauli massive gravity backgrounds, challenging the consistency of such theories as infrared modifications of GR.

Findings

Superluminal propagation occurs in nearly Minkowski backgrounds.

Superluminality appears within the effective theory's cutoff scale.

Fine-tuning may eliminate superluminality, but lacks symmetry protection.

Abstract

We study the propagation of helicity-1 gravitons in the Fierz--Pauli massive gravity in nearly Minkowski backgrounds. We show that, generically, there exist backgrounds consistent with field equations, in which the propagation is superluminal. The relevant distances are much longer than the ultraviolet cutoff length inherent in the Fierz--Pauli gravity, so superluminality occurs within the domain of validity of the effective low energy theory. There remains a possibility that one may get rid of this property by imposing fine tuning relations between the coefficients in the non-linear generalization of the Fierz--Pauli mass term, order by order in non-linearity; however, these relations are not protected by any obvious symmetry. Thus, among others, superluminality is a problematic property to worry about when attempting to construct infrared modifications of General Relativity.