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.
