We study the postinflationary dynamics of the Standard Model (SM) Higgs field in the presence of a nonminimal coupling $\xi |\mathrm{\Phi }{|}^{2}R$ to gravity, both with and without the electroweak gauge fields coupled to the Higgs field. 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 renormalization 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 $m_t\approx 173.3\mathrm{GeV}$, the Higgs vacuum instability is triggered for $\xi \gtrsim 4–5$, although a slightly lower mass of $m_t\approx 172.1\mathrm{GeV}$ 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 field-curvature coupling within the SM.

• Received 14 September 2017

DOI:https://doi.org/10.1103/PhysRevD.98.023532

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Published by the American Physical Society