Superluminality in the Fierz--Pauli massive gravity

Understand

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.