Simple Cosmological Solution to the Higgs Instability Problem in the
  Chaotic Inflation and Formation of Primordial Black Holes
  We revisit the compatibility between the chaotic inflation, which provides a
natural solution to the initial condition problem, and the metastable
electroweak vacuum, which is suggested by the results of LHC and the current
mass measurements of top quark and Higgs boson. It is known that the chaotic
inflation poses a threat to the stability of the electroweak vacuum because it
easily generates large Higgs fluctuations during inflation or preheating and
triggers the catastrophic vacuum decay. In this paper, we propose a simple
cosmological solution in which the vacuum is stabilized during chaotic
inflation, preheating and after that. This simple solution naturally predicts
the formation of primordial black holes. We find interesting parameter regions
where the present dark matter density is provided by them. Also, the thermal
leptogenesis can be accommodated in our scenario.
