Complete set of tree-level $2\to 2$ scattering amplitudes of ghost-free bimetric theory

Abstract

Bimetric theory is an extension of general relativity that perturbatively describes one massless and one massive graviton. It admits observationally viable cosmologies, passes local tests of gravity, and provides candidates for dynamical dark energy and spin-2 dark matter. Scattering amplitudes provide a complementary probe of its consistency, e.g. through analyticity, unitarity, and causality. While the tree-level $2\to2$ amplitudes of the closely related theory of massive gravity have previously been computed and analysed, the richer amplitude structure of bimetric theory has mostly been studied for selected processes and helicity sectors. We present the complete set of tree-level $2\to2$ scattering amplitudes of ghost-free bimetric theory around proportional Minkowski backgrounds. We expand the action through quartic order in the mass eigenstates and use a computer-algebra workflow to compute all of the $199$ symmetry-inequivalent helicity amplitudes. We find a clear hierarchy: amplitudes with a single massive external state vanish, those with exactly two are independent of the nonlinear bimetric parameters, and nonlinear ghost-free parameter dependence first appears with three massive external states. Taking the massive-gravity limit yields the complete set of tree-level $2\to2$ massive gravity amplitudes, which agree exactly with previous results. Finally, all amplitudes grow with energy at most as $E^6$, corresponding to the characteristic $Λ_3$ strong-coupling scale, and this maximal growth cannot be eliminated by any nontrivial choice of the theory parameters.