Dynamical Tuning of the Initial Condition in Small Field Inflations — Can We Testify the CW Mechanism in the Universe

I explain the cosmological consequence of the particle physics models with the Coleman–Weinberg (CW) type potential. Such particle physics models generally predict the small field inflation (SFI), but the SFI requires a very unnatural fine-tuning of the initial condi- tion. In this talk, I reviewed our proposal¹ to solve the fine-tuning problem dynamically by a trapping of the inflaton field due to the preheating before the SFI starts.