Critical Points in Palatini Higgs Inflation with Small Non-Minimal Coupling

TL;DR

This paper studies Higgs-driven inflation in the Palatini formulation with small non-minimal coupling, analyzing parameter effects and the potential for critical points, but finds challenges in matching observed CMB perturbations.

Contribution

It introduces a detailed analysis of Palatini Higgs inflation with small non-minimal coupling, incorporating Standard Model RG running and tunable parameters, revealing the presence of critical points affecting power spectrum.

Findings

Critical points can enhance the power spectrum.

Observed CMB amplitude cannot be achieved in this model.

Palatini Higgs inflation shows robustness against quantum corrections.

Abstract

We investigate inflation driven by the Higgs boson in the Palatini formulation of General Relativity. Our analysis primarily focuses on a small non-minimal coupling of the Higgs field to gravity in the range $0<\xi\lesssim 1$. We incorporate the renormalization group running of the relevant parameters as computed within the Standard Model and allow for small corrections. In addition to $\xi$, our model features two tunable parameters: the low-energy value of the top Yukawa coupling and an effective jump of the Higgs self-interaction. Our results indicate that critical points leading to a large enhancement of the power spectrum can be produced. However, the observed amplitude of perturbations in the CMB cannot be matched within this setting. On the one hand, this makes it difficult to generate a sizable abundance of primordial black holes. On the other hand, our finding can be viewed as further evidence that Palatini Higgs inflation has favourable high-energy properties due to robustness against quantum corrections.