A Universal Bound on the Strong Coupling Scale of a Gravitationally Coupled Massive Spin-2 Particle

TL;DR

This paper establishes a universal upper limit on the energy scale where a massive spin-2 particle coupled to gravity remains perturbatively consistent, with implications for bigravity and higher-spin theories.

Contribution

It provides a model-independent bound on the strong coupling scale for massive spin-2 particles coupled to gravity, using scattering amplitudes and unitarity constraints.

Findings

Maximum strong coupling scale is b3 (m^2 M_P)^{1/3} for ghost-free bigravity.

The scale can be raised to M_P with a wrong-sign kinetic term, as in quadratic curvature gravity.

Generalization to higher-spin particles suggests similar bounds and behaviors.

Abstract

We find a model-independent upper bound on the strong coupling scale for a massive spin-2 particle coupled to Einstein gravity. Our approach is to directly construct tree-level scattering amplitudes for these degrees of freedom and use them to find the maximum scale of perturbative unitarity violation. The highest scale is $\Lambda_3=\left(m^2M_P\right)^{1/3}$, which is saturated by ghost-free bigravity. The strong coupling scale can be further raised to $M_P$ if the kinetic term for one particle has the wrong sign, which uniquely gives the amplitudes of quadratic curvature gravity. We also discuss the generalization to massive higher-spin particles coupled to gravity.