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

TL;DR

This paper investigates tree-level unitarity limits in Higgs inflation models within metric and Palatini gravity formulations, analyzing scattering amplitudes and comparing unitarity violation scales during electroweak vacuum and inflation.

Contribution

It provides a detailed calculation of unitarity bounds for Higgs inflation in both gravity formulations, including collider constraints on the non-minimal coupling parameter.

Findings

Unitarity is violated at ~M_Planck/ξ in metric formulation at electroweak vacuum.

Unitarity is violated at ~M_Planck/√ξ in Palatini formulation at electroweak vacuum.

Unitarity limit during inflation is at ~M_Planck/√ξ in both formulations.

Abstract

We calculate the tree-level amplitudes for electrically neutral $2\to2$ 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, $\xi<2.5\times10^{31}$.