Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments

Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GWevents as mergers of PBHs that are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs, and thus we have several other probes to test this scenario. We point out that the current pulsar timing array ( PTA) experiments already put severe constraints on GWs generated via the second-order effects, and that the observation of the cosmic microwave background puts severe restriction on its ae distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at k similar to 10(6) Mpc(-1) to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the ae distortion. We propose a mechanism that can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded.