Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation

We calculate the tree-level amplitudes for electrically neutral 2 -> 2 scattering for the Standard Model Higgs doublet non-minimally coupled to the Ricci scalar. We consider both the metric and the Palatini formulation of gravity. We find the partial wave unitarity limit for a general background field value. Our results are in agreement with previous work. In the electroweak vacuum, tree-level unitarity is violated at similar to M-Pl/xi in the metric formulation, and at similar to MPl/root xi in the Palatini formulation. In the inflationary large field background, the unitarity limit is at similar to MPl/root xi in both formulations. We compare the unitarity violation energy to scales relevant during inflation. We also calculate a direct collider limit on xi in the Palatini formulation, xi < 2.5 x 10(31).Peer reviewe