Gravitational-Wave Constraints on the Abundance of Primordial Black Holes

We investigate the features of gravitational waves (GWs) induced by primordial density fluctuations with a large amplitude peak associated with the formation of primordial black holes (PBHs). It is shown that the spectrum of induced GW is insensitive to the width of the peak in wavenumber space provided it is below a certain value, but the amplitude of the spectrum decreases at the peak frequency and decreases faster at low frequencies for a larger width. A correspondence between the GW amplitude and PBH abundance is also investigated incorporating the peak width. We find that PBHs with masses of 1020-26 g can be probed using space-based laser interferometers and atomic interferometers even if the peak width is large. Moreover we obtain constraints on the abundance of the supermassive PBHs by comparing a low-frequency tail of the GW spectrum with CMB observations.