Massive and Massless Spin-2 Scattering and Asymptotic Superluminality

TL;DR

This work derives model-independent constraints on the cubic interactions of a massive and a massless spin-2 field by demanding positivity of the eikonal phase in 2-to-2 scattering, thereby excluding time advances at asymptotic times. The analysis shows that, under a parametric gap to new physics, the allowed cubic vertices are restricted to Einstein–Hilbert–type structures, with additional restrictions on how these fields couple to matter. In ghost-free bi-gravity, the combined constraints reduce the two-parameter family to a unique one-parameter subfamily possessing a Z2 symmetry between the two metrics, and they constrain matter couplings via an S-matrix equivalence principle. The results are corroborated by classical shockwave (Shapiro delay) calculations in bi-gravity, connecting high-energy S-matrix constraints to classical propagation and offering insight into UV completion and consistency of higher-spin interactions with gravity.

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.

Figures (2)

• Figure 1: Plot of the allowed parameters that satisfy the inequalities \ref{['constraint']}.
• Figure 2: A plot of the allowed parameter space for the coupling constant $\alpha_m=\kappa_m \frac{M_*^2}{2 M_f M_g}$ and the ratio $M_g/M_f$. The shaded region corresponds to the allowed parameter space. The different curves correspond to different matter couplings: coupling to the $g$ metric only (blue, dotted), to the $f$ metric only (orange, long dash), equally to both metrics (green, solid), to the massless eigenstate only (pink, dot dashed), and equal coupling to both the massive and massless eigenstates (yellow, short dash). The information contained in this plot is equivalent to that in Figure \ref{['fig:ineqplot']}, but these variables are the ones that arise naturally in bimetric gravity.