Constraints on Compact Dark Matters Population from microlensing Effect of Gravitational Wave for the third-generation gravitational Wave Detector

Since the first direct detection of gravitational waves (GWs) from a binary black-hole merger by the LIGO-Virgo Collaboration, GWs have emerged as a powerful probe of astrophysics and cosmology. If extragalactic compact dark matter (DM) candidates, such as primordial black holes, constitute a non-negligible fraction of the DM component over a broad mass range, they can imprint distinctive microlensing signatures on GW signals. In this work, we develop a framework to infer the population properties of extragalactic compact DM by simulating microlensing GWs in the frequency band of the third-generation ground-based GW detector, the Einstein Telescope, and analyzing them via hierarchical Bayesian inference. For a population described by a power-law mass function, we show that the detection of only several microlensing GW events among $10^4$ binary black-hole coalescences can constrain the compact DMs abundance to the level of $\sim 10^{-3}$. This forecast demonstrates that searching for and identifying microlensing signatures in future GW observations can provide a complementary approach to constraining compact DM scenarios.