Electroweak Vacuum Stabilized by Moduli during/after Inflation
  It is known that the present electroweak vacuum is likely to be metastable and it may lead to a serious instability during/after inflation. We propose a simple solution to the problem of vacuum instability during/after inflation. If there is a moduli field which has Planck-suppressed interactions with the standard model fields, the Higgs quartic coupling in the early universe naturally takes a different value from the present one. A slight change of the quartic coupling in the early universe makes the Higgs potential absolutely stable and hence we are free from the vacuum instability during/after inflation. 
Yohei Ema, Kyohei Mukaida, Kazunori Nakayama
hep-ph astro-ph.CO