Gravitational-Wave Constraints on the Abundance of Primordial Black
  Holes
  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. Further we obtain constraints on the
abundance of the supermassive PBHs by comparing a low frequency tail of the GW
spectrum with CMB observations.
