Quantum Corrections to Higgs Inflation in Einstein-Cartan Gravity

TL;DR

This paper investigates quantum corrections to Higgs inflation within Einstein-Cartan gravity, revealing how induced $ R^2 $ terms and the scalaron extend the model's UV behavior and address potential strong coupling issues.

Contribution

It demonstrates that quantum corrections induce a scalaron in Einstein-Cartan Higgs inflation, extending the UV cutoff and connecting metric and Palatini formalisms.

Findings

Induction of a scalaron due to $ R^2 $ terms in Einstein-Cartan formalism.

Scalaron decouples near the Palatini limit, affecting UV extension.

Potential resolution of strong coupling problems during reheating.

Abstract

This paper studies the quantum corrections to the Higgs inflation model in the context of the Einstein-Cartan (E-C) gravity in the large-$ N $ limit with $N$ being the number of real scalar components in Higgs. Recently, it is realized that the Higgs inflation in the E-C formalism smoothly connects those in the metric and the Palatini formalisms in the presence of a non-minimal coupling between the Higgs fields and the Nieh-Yan term. This motivates us to investigate the quantum corrections to the E-C Higgs inflation and to clarify how the Ricci curvature squared $ R^2 $ induced by the quantum corrections succeeds in Ultraviolet (UV)-extending the Higgs inflation in metric formalism while it fails in the Palatini case. We show that a generalized $ R^2 $-term required for the renormalization in the E-C formalism induces a new scalar degree of freedom (DoF), the scalaron, which gradually decouples with the system due to its increasing mass as approaching the Palatini limit. The presence of the scalaron extends the UV cutoff at vacuum of the original model except for the parameter space close to the Palatini limit. This UV-extension is expected to solve the strong coupling problem that may exist during (p)reheating in the absence of the scalaron.