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.