Gravitational corrections to electroweak vacuum decay: metric vs. Palatini

TL;DR

This paper compares gravitational effects on electroweak vacuum stability in metric and Palatini formalisms, revealing that gravity's suppressive effect on decay is milder in Palatini and establishing a lower bound on the nonminimal coupling for unitarity.

Contribution

It analytically distinguishes the impact of gravitational corrections on vacuum decay in metric versus Palatini gravity, introducing a perturbative approach and identifying bounds on the coupling.

Findings

Gravity suppresses vacuum decay less in Palatini than in metric formalism.

Positivity of gravitational corrections requires ta > -1/12 in Palatini.

Lower bound on nonminimal coupling ta for unitarity in Palatini.

Abstract

We consider the standard Einstein-Hilbert-Higgs action where the Higgs field couples nonminimally with gravity via the term $\xi h^2 \mathcal{R}$, and investigate the stability of the electroweak vacuum in the presence of gravitational corrections in both the metric and Palatini formulations of gravity. In order to identify the differences between the two formalisms analytically, we follow a perturbative approach in which the gravitational corrections are taken into consideration via a leading order expansion in the gravitational coupling constant. Our analysis shows that in the Palatini formalism, the well-known effect of gravity suppressing the vacuum decay probability, becomes milder in comparison with the metric case for any value of the nonminimal coupling $\xi$. Furthermore, we have found that in the Palatini formalism, the positivity of the gravitational corrections, which is a necessary requirement for the unitarity of the theory, entails the lower bound $\xi>-1/12$.