Instability of the Electroweak Vacuum in Starobinsky Inflation

TL;DR

This paper investigates the stability of the electroweak vacuum during Starobinsky inflation, focusing on the effects of the non-minimal Higgs coupling and deriving bounds to prevent vacuum decay.

Contribution

It provides a detailed numerical analysis of Higgs field evolution during preheating in Starobinsky inflation, establishing new upper bounds on the non-minimal coupling constant.

Findings

The non-minimal coupling bound is more stringent in Starobinsky inflation.

Higgs amplitude can be amplified via parametric resonance after inflation.

The study constrains the coupling to ensure vacuum stability.

Abstract

We study the stability of the electroweak vacuum during and after the Starobinsky inflation, assuming the existence of the non-minimal Higgs coupling to the Ricci scalar. In the Starobinsky inflation, there exists $R^2$ term (with $R$ being the Ricci scalar), which modifies the evolution equation of the Higgs field. We consider the case that the non-minimal coupling is sizable so that the quantum fluctuation of the Higgs field is suppressed and that the Higgs amplitude is settled near the origin during the inflation. In such a case, the Higgs amplitude may be amplified in the preheating epoch after inflation because of the parametric resonance due to the non-minimal coupling. We perform a detailed analysis of the evolution of the Higgs field in the preheating epoch by a numerical lattice simulation and derive an upper bound on the non-minimal coupling constant $\xi$ in order to realize the electroweak vacuum in the present universe. We find that the upper bound on $\xi$ in the Starobinsky inflation model is more stringent than that in conventional inflation models without the $R^2$ term.