Prospective constraints on the primordial black hole abundance from the stochastic gravitational-wave backgrounds produced by coalescing events and curvature perturbations

For a variety of on-going and planned gravitational-wave (GW) experiments, we study expected constraints on the fraction ($f_{\mathrm{P}\mathrm{B}\mathrm{H}}$) of primordial black holes (PBHs) in dark matter by evaluating the energy-density spectra of two kinds of stochastic GW backgrounds. The first one is produced from an incoherent superposition of GWs emitted from coalescences of all the binary PBHs. The second one is induced through non-linear mode couplings of large primordial curvature perturbations inevitably associated with the generation of PBHs in the early Universe. In this paper, we focus on the PBHs with their masses of ${10}^{-8}{M}_{\odot }\le M_{\mathrm{P}\mathrm{B}\mathrm{H}}<1M_{\odot }$, since they are not expected to be of a stellar origin. In almost all ranges of the masses, we show that the experiments are sensitive to constrain the fraction for $10^{-5} \lesssim f_{\rm PBH} \lesssim 1$ by considering the GWs from coalescing events and ${10}^{-13}\lesssim f_{\mathrm{P}\mathrm{B}\mathrm{H}}\lesssim 1$ by considering the GWs from curvature perturbations. Exceptionally, only in a narrow range of masses for $M_{\mathrm{P}\mathrm{B}\mathrm{H}}\simeq {10}^{-7}{M}_{\odot }$, the fraction cannot be constrained for $f_{\mathrm{P}\mathrm{B}\mathrm{H}}\lesssim {10}^{-13}$ by those two GW backgrounds.