Constraining the Primordial Black Hole Abundance with Space-Based Detectors

Overdense regions can collapse into primordial black holes (PBHs) in the early universe, which are a compelling candidate for dark matter. Current constraints leave the asteroid-mass window the only possible one for PBH to account for all the dark matter, which can only be probed indirectly by the scalar-induced gravitational waves (GWs) sourced by the curvature perturbation which forms PBH. In this work, we explore the capabilities of future space-based gravitational wave detectors, including LISA, Taiji, and TianQin, to constrain such induced GWs as well as the PBH abundance. We systematically account for the width of the primordial curvature power spectrum, and find that the asteroid-mass window can be fully probed by all three space-based interferometers. If PBHs constitute the majority of dark matter, the induced GW leaves a strong signal in the mHz band with a signal-to-noise ratio of $10^3$--$10^4$.