Prospects for probing ultralight primordial black holes using the
  stochastic gravitational-wave background induced by primordial curvature
  perturbations
  Ultralight primordial black holes (PBHs) with masses $\lesssim 10^{15}$g and
subatomic Schwarzschild radii, produced in the early Universe, are expected to
have evaporated by the current cosmic age due to Hawking radiation. Based on
this assumption, a number of constraints on the abundance of ultralight PBHs
have been made. However, Hawking radiation has thus far not been verified
experimentally. It would, therefore, be of interest if constraints on
ultralight PBHs could be placed independent of the assumption of
Hawking-radiation. In this paper, we explore the possibility of probing these
PBHs, within a narrow mass range, using gravitational-wave (GW) data from the
two LIGO detectors. The idea is that large primordial curvature perturbations
that result in the formation of PBHs, would also generate GWs through
non-linear mode couplings. These induced GWs would produce a stochastic
background. Specifically, we focus our attention on PBHs of mass range $\sim
10^{13} - 10^{15}$g for which the induced stochastic GW background peak falls
in the sensitivity band of LIGO. We find that, for both narrow and broad
Gaussian PBH mass distributions, the corresponding GW background would be
detectable using presently available LIGO data, provided we neglect the
existing constraints on the abundance of PBHs, which are based on Hawking
radiation. Furthermore, we find that these stochastic backgrounds would be
detectable in LIGO's third observing run, even after considering the existing
constraints on PBH abundance. A non-detection should enable us to constrain the
amplitude of primordial curvature perturbations as well as the abundance of
ultralight PBHs. We estimate that by the end of the third observing run,
assuming non-detection, we should be able to place constraints that are orders
of magnitude better than currently existing ones.
