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.
Highlights
The Standard Model (SM) potential may become negative at very high energies [1,2]
II, we present a brief review of the inflaton and Higgs dynamics after inflation in the presence of a Higgs field-curvature nonminimal coupling
We have studied the postinflationary dynamics of the Standard Model Higgs field with lattice simulations, in the case where it possesses a nonminimal coupling ξ to gravity
Summary
The Standard Model (SM) potential may become negative at very high energies [1,2]. This has prompted an important effort to determine whether the electroweak vacuum is, in the present, stable or unstable. One simple way to prevent this from happening is to consider a sufficiently low inflationary scale, so that even if the Higgs field is excited during inflation, its amplitude never reaches the potential barrier Another way of ensuring vacuum stability is to consider values of the top-quark mass 2–3 sigma below its central value mt 1⁄4 172.44ÆÆ00..1437ððsstyasttÞÞ GeV [24], so that the second minimum in the Higgs potential is either shifted to sufficiently high energies or is not present. We refer to the reduced Planck mass as mp 1⁄4 ð8πGÞ−1=2 ≃ 2.44 × 1018 GeV
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