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

Abstract

Abstract 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 ∼ MPl/ξ in the metric formulation, and at $$ \sim {M}_{\mathrm{P}1}/\sqrt{\xi } $$ ∼ M P 1 / ξ in the Palatini formulation. In the inflationary large field background, the unitarity limit is at $$ \sim {M}_{\mathrm{P}1}/\sqrt{\xi } $$ ∼ M P 1 / ξ in both formulations. We compare the unitarity violation energy to scales relevant during inflation. We also calculate a direct collider limit on ξ in the Palatini formulation, ξ < 2.5 × 1031.