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

Abstract

We calculate the tree-level amplitudes for electrically neutral $2\to 2$ 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 $\sim M_{\text{Planck}}/\xi$ in the metric formulation, and at $\sim M_{\text{Planck}}/\sqrt{\xi }$ in the Palatini formulation. In the inflationary large field background, the unitarity limit is at $\sim M_{\text{Planck}}/\sqrt{\xi }$ 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, $\xi <2.5\times 10^{31}$.

Comments: 15+8 pages, 3 figures. v2: Corrected calculation, significant change in the metric case results. Added references, removed one reference. v3: Corrected typos. Published version