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;4M₌₈₃₃₋₄ ₃₎ₓ ₈₍ ₂₈ₑ₂₋₄, 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.