Double Inflation in Classically Conformal $B-L$ Model

It has recently been shown in Ref. [1] that the double-inflation scenario based on the Coleman-Weinberg potential can successfully generate primordial black holes (PBHs) with the inflationary predictions consistent with the Planck measurements. These PBHs can play the role of dark matter in our universe. In this paper, we propose the classically conformal minimal $B-L$ model as an ultra-violet (UV) completion of the scenario. In our model, the $B-L$ Higgs field is identified with the inflaton and the electroweak symmetry breaking is triggered by the radiative $B-L$ symmetry breaking with the Coleman-Weinberg potential. We show that this UV completion leads to a viable cosmological history after the double inflaton: the universe is reheated via inflaton decay into right-handed neutrinos whose mass is determined consistently by a relation between the number of e-folds and reheating temperature. Using the general parameterization for neutrino Dirac Yukawa couplings through the seesaw mechanism and the neutrino oscillation data, we also show that the observed baryon asymmetry of the universe is successfully reproduced by either resonant leptogenesis or non-thermal leptogenesis. Based on the scalar power spectrum shown in Ref. [1], we evaluate the scalar induced gravitational wave spectrum, which can be tested by various proposed gravitational wave observatories like BBO, DECIGO etc.