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Title: Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
Authors: Ito, Asuka 
Khater, Wafaa 
Rasanen, Syksy 
Keywords: Astro-ph.CO;Polarization (Nuclear physics);Quantum cosmology;Particles (Nuclear physics);High energy physics;General relativity (Physics);Phenomenology;Cosmology of Theories BSM;Early Universe Particle Physics
Issue Date: 10-Jun-2022
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, $\xi<2.5\times10^{31}$.
Description: 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
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