# Electroweak stability and non-minimal coupling

## TL;DR

This paper investigates how a non-minimal Higgs-curvature coupling can stabilize the electroweak vacuum during inflation and preheating, analyzing particle production effects and vacuum stability depending on coupling strength.

## Contribution

It provides a detailed analysis of Higgs particle production during preheating with non-minimal coupling, highlighting the importance of adiabatic vacuum choices and coupling strength.

## Key findings

- Large coupling leads to efficient Higgs decay to the true vacuum.
- Vacuum dependence increases over time, affecting stability analysis.
- Small coupling results are inconclusive due to vacuum dependence.

## Abstract

The measured values of the Higgs and top quark mass indicate that the electroweak vacuum is metastable if there is no new physics below the Planck scale. This is at odds with a period of high scale inflation. A non-minimal coupling between the Higgs field and the Ricci scalar can stabilize the vacuum as it generates a large effective Higgs mass during inflation. We consider the effect of this coupling during preheating, when Higgs modes can be produced very efficiently due to the oscillating Ricci scalar. We compute their effect on the effective potential and the energy density. The Higgs excitations are defined with respect to the adiabatic vacuum. We study the adiabaticity conditions and find that the dependence of our results on the choice of the order of the adiabatic vacuum increases with time. For large enough coupling particle production is so efficient that the Higgs decays to the true vacuum before this is an issue. However, for smaller values of the Higgs-curvature coupling no definite statements can be made as the vacuum dependence is large.