Gravitational-Wave Constraints on the Abundance of Primordial Black Holes

Understand

We investigate features of Gravitational Waves (GWs) induced by primordial density fluctuations with a large amplitude peak associated with 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 reduces 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 10^{20-26}g can be probed by space-based laser interferometers and atomic interferometers irrespective of whether the peak width is small or not.