Gravitational-wave background as a probe of the primordial black-hole abundance

The formation of a significant number of black holes (PBHs) is realized if and only if primordial density fluctuations have a large amplitude, which means that tensor perturbations generated from these scalar perturbations as a second-order effect are also large and comparable to the observational data. We show that pulsar timing data essentially rule out PBHs with 10;{2}-10;{4}M_{middle dot in circle}, which were previously considered as a candidate of intermediate-mass black holes, and that PBHs with a mass range of 10;{20} to 10;{26} g, which serves as a candidate of dark matter, may be probed by future space-based laser interferometers and atomic interferometers.