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

We calculate the tree-level amplitudes for electrically neutral $2\to2$ scattering Standard Model Higgs doublet non-minimally coupled to Ricci scalar. consider both metric and Palatini formulation of gravity. find partial wave unitarity limit a general background field value. Our results are in agreement with previous work. In electroweak vacuum, is violated at $\sim M_\text{Planck}/\xi$ formulation, M_\text{Planck}/\sqrt{\xi}$ formulation. inflationary large background, formulations. compare violation energy scales relevant during inflation. also direct collider on $\xi$ $\xi<2.5\times10^{31}$.