Gravitational wave background as a probe of the primordial black hole abundance

TL;DR

It is shown that pulsar timing data essentially rule out PBHs with 10;{2}-10;{4}M_{middle dot in circle}, which were previously considered as a candidate of intermediate-mass black holes, and that PBHS with a mass range of 10;20 to 10;26 g, which serves as a candidates of dark matter, may be probed by future space-based laser interferometers and atomic interferometer.

Abstract

Formation of significant number of primordial black holes (PBHs) is realized if and only if primordial density fluctuations have a large amplitude, which means that tensor perturbations generated from these scalar perturbations as a second order effect are also large and comparable to the observational data. We show that pulsar timing observation could find/rule out PBHs with \sim 10^2 M_solar which are considered as a candidate of intermediate-mass black holes and that PBHs with mass range 10^{20-26} g, which serves as a candidate of dark matter, may be probed by future space-based laser interferometers and atomic interferometers.

Figures (2)

• Figure 1: Energy density of scalar-induced GWs associated with PBH formation together with current pulsar constraint (thick solid line segment) and sensitivity of various GW detectors (convex curves). Left and right wedge-shaped curves indicate expected power spectra of GWs from two different peaked scalar fluctuations corresponding to $(\Omega_{\mathrm{PBH}}h^2,M_{\mathrm{PBH}},g_{\ast p}) =(10^{-5},30M_{\odot},10.75)$ (left) and $(10^{-1},10^{20}\mathrm{g}, 106.75)$ (right), respectively. The red dotted (green broken) line shows an envelope curve, $A_{\mathrm{GW}}$, corresponding to $\Omega_{\mathrm{PBH}}=10^{-1}$ ($10^{-5}$) obtained by moving $k_p$ and ${\cal A}$, which depend on the frequency logarithmically except for the discontinuities due to the change of the relativistic degrees of freedom at the QCD phase transition and the electron-positron pair annihilation.
• Figure 2: New constraints on the mass spectrum of PBHs imposed by scalar-generated GWs. Dotted line represents the mass range to be constrained by future GW detectors.