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, $\xi <2.5\times 10^{31}$.

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

References in corpus (45)

• The Standard Model Higgs boson as the inflaton
• Higgs inflation: consistency and generalisations
• Inflation scenario via the Standard Model Higgs boson and LHC
• Power-counting and the Validity of the Classical Approximation During Inflation
• On Inflation with Non-minimal Coupling
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Cosmological implications of the Higgs mass measurement
• Higgs inflation at the critical point
• Higgs inflation still alive
• Higgs-Palatini Inflation and Unitarity
• Higgs G-inflation
• Equivalence of the Einstein and Jordan frames
• The Higgs Phenomenon in Quantum Gravity
• Higgs inflation with loop corrections in the Palatini formulation
• Violent Preheating in Inflation with Nonminimal Coupling
• Preheating in Palatini Higgs inflation
• A Unitarity-Conserving Higgs Inflation Model
• Higgs inflation with the Holst and the Nieh-Yan term
• Remarks on Higgs Inflation
• What is the Top Quark Mass?
• On the geometrical interpretation of scale-invariant models of inflation
• Higgs Gravitational Interaction, Weak Boson Scattering, and Higgs Inflation in Jordan and Einstein Frames
• Palatini-Higgs inflation with non-minimal derivative coupling
• Canonical Gravity with Fermions
• Gauge-Independent Scales Related to the Standard Model Vacuum Instability
• Frame Covariant Nonminimal Multifield Inflation
• Higgs inflation in Einstein-Cartan gravity
• Occurrence of Tachyonic Preheating in the Mixed Higgs-$R^2$ Model
• Einstein-Cartan Portal to Dark Matter
• Higgs inflation and teleparallel gravity
• Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
• Einstein-Cartan gravity, matter, and scale-invariant generalization
• Critical point Higgs inflation in the Palatini formulation
• On UV-completion of Palatini-Higgs inflation
• Self-unitarization of New Higgs Inflation and compatibility with Planck and BICEP2 data
• Does Palatini Higgs Inflation Conserve Unitarity?
• A heatwave affair: mixed Higgs-$R^2$ preheating on the lattice
• On Preheating in Higgs Inflation
• Non-local self-healing of Higgs inflation
• Successful Higgs inflation from combined nonminimal and derivative couplings
• Ultraviolet behaviour of Higgs inflation models
• Cosmological Constraints on the Higgs Boson Mass
• Matching and running sensitivity in non-renormalizable inflationary models
• Equivalence of Einstein and Jordan frames in quantized cosmological models
• On the Cosmological Frame Problem

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• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Baryogenesis from combined Higgs - scalar field inflation
• Beyond (and back to) Palatini quadratic gravity and inflation
• Alternative approach to the Starobinsky model for inflation scenarios
• $\tilde{\xi }$-attractors in metric-affine gravity
• Hybrid metric-Palatini Higgs inflation
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Baryogenesis from Higgs Inflation
• Higgs-dilaton model revisited: can dilaton act as QCD axion?
• Induced-Gravity Palatini-Like Higgs Inflation in Supergravity Confronts ACT DR6
• Natural inflation in Palatini $F(R,X)$
• (Lovelock)${}^2$ inflation: explaining the ACT data and equivalence to Higgs-Gauss-Bonnet inflation