Primordial black holes under the double inflationary power spectrum

Recently, it has been shown that the primordial black holes (PBHs) produced by near critical collapse in the expanding universe have a scaling mass relation similar to that of black holes produced in asymptotically flat spacetime. Distinct from PBHs formed with a mass about the size of the horizon mass (type I), the PBHs with the scaling relation (type II) can be created with a range of masses at a given formation time. In general, only the case in which the PBH formation is concentrated at one epoch has been considered. However, it is expected that PBH formation is possible over a broad range of epochs if the density fluctuation has a rather large amplitude and smooth scale dependence. In this paper, we study the PBH formation for both types assuming the power spectrum of double inflationary models in which the small scale fluctuations could have large amplitudes independent of the CMBR anisotropy. The mass spectrum of type II PBHs is newly constructed without limiting the PBH formation period. The double inflationary power spectrum is assumed to be of double simple power law which are smoothly connected. Under the assumed power spectrum, the accumulation of small PBHs formed at later times is important and the mass range is significantly broadened for both types. The PBH mass spectra are far smoother than the observed MACHO spectrum due to our assumption of a smooth spectrum. In order to fit the observation, a more spiky spectrum is required.