Universal bound on the strong coupling scale of a gravitationally coupled massive spin-2 particle

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 Λ3=(m2MP)1/3, which is saturated by ghost-free bigravity. The strong coupling scale can be further raised to MP 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.