Higgs-curvature coupling and post-inflationary vacuum instability

TL;DR

This paper investigates how the Higgs-curvature coupling affects the stability of the Higgs vacuum after inflation, deriving bounds on the coupling constant based on lattice simulations and experimental uncertainties.

Contribution

It provides the first detailed bounds on the Higgs-curvature coupling considering electroweak gauge fields and inflationary dynamics within the Standard Model.

Findings

Higgs vacuum stability constrains the coupling to be below ~5 for certain top-quark masses.

Electroweak gauge fields have minimal impact on the bounds.

Instability develops within a specific timeframe depending on the top-quark mass.

Abstract

We study the post-inflationary dynamics of the Standard Model (SM) Higgs field in the presence of a non-minimal coupling $\xi|\Phi|^2R$ to gravity, both with and without the electroweak gauge fields coupled to the Higgs. We assume a minimal scenario in which inflation and reheating are caused by chaotic inflation with a quadratic potential, and no additional new physics is relevant below the Planck scale. By using classical real-time lattice simulations with a renormalisation group improved effective Higgs potential and by demanding the stability of the Higgs vacuum after inflation, we obtain upper bounds for $\xi$, taking into account the experimental uncertainty of the top-Yukawa coupling. We compare the bounds in the absence and presence of the electroweak gauge bosons, and conclude that the addition of gauge interactions has a rather minimal impact. In the unstable cases, we parametrize the time when such instability develops. For a top-quark mass $m_t \approx173.3 {\rm GeV}$, the Higgs vacuum instability is triggered for $\xi \gtrsim 4 -5$, although a slightly lower mass of $m_t \approx 172.1 {\rm GeV}$ pushes up this limit to $\xi \gtrsim 11 - 12$. This, together with the estimation $\xi \gtrsim 0.06$ for stability during inflation, provides tight constraints to the Higgs-curvature coupling within the SM.