On the Weyl gravity extension of Higgs inflation

TL;DR

This paper explores embedding Higgs inflation into Weyl gravity, showing it alleviates unitarity issues, introduces a light Weyl gauge field, and connects to Palatini and Higgs-like inflation models with potential observable signatures.

Contribution

It demonstrates how Weyl gravity embedding modifies Higgs inflation, introduces a light Weyl gauge field, and unifies different inflation formulations with testable Higgs physics signatures.

Findings

Unitarity problem of Higgs inflation is mitigated in Weyl gravity.

The model aligns with Palatini Higgs inflation but includes a light Weyl gauge field.

Potential observable effects include suppressed Higgs couplings and direct Weyl gauge interactions.

Abstract

We consider the embedding of Higgs inflation with a non-minimal coupling into the Weyl gravity. In this model, the effective current-current interactions from the heavy Weyl gauge field cancel the non-canonical Higgs kinetic term in Einstein frame, so the unitarity problem of the original Higgs inflation becomes less severe. For a simple case where the couplings of the heavy Weyl gauge field appears from the non-minimal couplings to the Ricci curvature scalar in Weyl gravity, we find that the resultant model for Higgs inflation is the same as in the Palatini formulation for Higgs inflation. The crucial difference of our model from the Palatini formulation for Higgs inflation is that there is a light Weyl gauge field coupled to the Higgs fields. We also generalize the unitarization of Higgs inflation with general covariant kinetic terms for the dilaton and the Higgs fields, and realize a successful Higgs inflation, interpolating between the Palatini formulation for Higgs inflation and a Higgs-like inflation. We also discuss the Higgs mechanism for the light Weyl gauge field with an extra singlet scalar and show some interesting signatures for Higgs physics, such as the overall suppression of Higgs couplings and the direct couplings of the light Weyl gauge field to the Higgs boson.