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Primordial black holes (PBHs) are one of the candidates to explain thegravitational wave (GW) signals observed by the LIGO detectors. Among severalphenomena in the early Universe, cosmic inflation is a major example togenerate PBHs from large primordial density perturbations. In this paper, wediscuss the possibility to interpret the observed GW events as mergers of PBHswhich are produced by cosmic inflation. The primordial curvature perturbationshould be large enough to produce a sizable amount of PBHs and thus we haveseveral other probes to test this scenario. We point out that the currentpulsar timing array (PTA) experiments already put severe constraints on GWsgenerated via the second-order effects, and that the observation of the cosmicmicrowave background (CMB) puts severe restriction on its $\mu$ distortion. Inparticular, it is found that the scalar power spectrum should have a very sharppeak at $k \sim 10^{6}$ Mpc$^{-1}$ to fulfill the required abundance of PBHswhile evading constraints from the PTA experiments together with the $\mu$distortion. We propose a mechanism which can realize such a sharp peak. In thefuture, simple inflation models that generate PBHs via almost Gaussianfluctuations could be probed/excluded.

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