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Higgs vacuum metastability in primordial inflation, preheating, and reheating

Current measurements of the Higgs boson mass and top Yukawa coupling suggest that the effective Higgs potential develops an instability below the Planck scale. If the energy scale of inflation is as high as the GUT scale, inflationary quantum fluctuations of the Higgs field can easily destabilize the standard electroweak vacuum and produce a lot of AdS domains. This destabilization during inflation can be avoided if a relatively large nonminimal Higgs-gravity or inflaton-Higgs coupling is introduced. Such couplings generate a large effective mass term for the Higgs, which can raise the effective Higgs potential and suppress the vacuum fluctuation of the Higgs field. After primordial inflation, however, such effective masses drops rapidly and the nonminimal Higgs-gravity or inflaton-Higgs coupling can cause large fluctuations of the Higgs field to be generated via parametric resonance, thus producing AdS domains in the preheating stage. Furthermore, thermal fluctuations of the Higgs field cannot be neglected in the proceeding reheating epoch. We discuss the Higgs vacuum fluctuations during inflation, preheating, and reheating, and show that the Higgs metastability problem is severe unless the energy scale of the inflaton potential is much lower than the GUT scale.