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

Abstract

For a variety of ongoing and planned gravitational-wave (GW) experiments, we study expected constraints on the fraction (${f}_{\mathrm{PBH}}$) 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 of the binary PBHs. The second one is induced through nonlinear mode couplings of large primordial curvature perturbations inevitably associated with the generation of PBHs in the early Universe. In this paper, we focus on PBHs with masses ${10}^{\ensuremath{-}8}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\le}{M}_{\mathrm{PBH}}l1\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, since they are not expected to be of stellar origin. In almost all mass ranges, we show that the experiments are sensitive enough to constrain the fraction for ${10}^{\ensuremath{-}5}\ensuremath{\lesssim}{f}_{\mathrm{PBH}}\ensuremath{\lesssim}1$ by considering the GWs from coalescing events and ${10}^{\ensuremath{-}13}\ensuremath{\lesssim}{f}_{\mathrm{PBH}}\ensuremath{\lesssim}1$ by considering the GWs from curvature perturbations. Exceptionally, the fraction cannot be constrained for ${f}_{\mathrm{PBH}}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$ by these two GW backgrounds only in the narrow mass range around ${M}_{\mathrm{PBH}}\ensuremath{\simeq}{10}^{\ensuremath{-}7}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$.