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 less than or similar to 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 independently 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 nonlinear mode couplings. These induced GWs would produce a stochastic background. Specifically, we focus our attention on PBHs of the mass range similar to 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 nondetection 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 nondetection, we should be able to place constraints that are orders of magnitude better than currently existing ones.