Massive and Massless Spin-2 Scattering and Asymptotic Superluminality

TL;DR

This paper uses S-matrix analysis to derive model-independent constraints on cubic vertices in theories with massive and massless spin-2 particles, ensuring subluminal scattering and consistency with ghost-free bimetric gravity.

Contribution

It provides the first model-independent constraints on cubic vertices for massive and massless spin-2 particles, linking subluminality to specific vertex combinations and matter couplings.

Findings

Subleading cubic vertices must follow a specific linear combination for subluminality.

A one-parameter family of ghost-free bimetric theories is consistent with subluminal scattering.

Additional matter couplings are constrained by subluminality, confirmed via classical shockwave scattering.

Abstract

We constrain theories of a massive spin-2 particle coupled to a massless spin-2 particle by demanding the absence of a time advance in eikonal scattering. This is an $S$-matrix consideration that leads to model-independent constraints on the cubic vertices present in the theory. Of the possible cubic vertices for the two spin-2 particles, the requirement of subluminality leaves a particular linear combination of cubic vertices of the Einstein--Hilbert type. Either the cubic vertices must appear in this combination or new physics must enter at a scale parametrically the same as the mass of the massive spin-2 field. These conclusions imply that there is a one-parameter family of ghost-free bimetric theories of gravity that are consistent with subluminal scattering. When both particles couple to additional matter, subluminality places additional constraints on the matter couplings. We additionally reproduce these constraints by considering classical scattering off of a shockwave background in the ghost-free bimetric theory.