Constraints on compact dark matter from lensing of gravitational waves for the third-generation gravitational wave detector

Since the first gravitational wave (GW) event from binary black hole (BBH) was detected by LIGO-Virgo, GWs have become a useful probe on astrophysics and cosmology. If compact dark matter (DM) objects e.g. primordial black holes, contribute a significant fraction of dark matter at wide mass range, they will cause microlensing in the GW signals with long wavelengths that are distinct from the lensing effects of electromagnetic signals from astrophysical objects. In this paper, we apply the lensing effect of GW from BBH to derive constraints on the abundance of compact DM for the Cosmic Explorer, a third-generation ground-based GW detector. We firstly consider two channels of formation of BBH that contribute to low and high redshift GW sources, including the astrophysical origin BBH scenario, and the primordial origin BBH scenario. Secondly, comparing with the method of optical depth, we use the Bayesian analysis to derive constraints on the abundance of compact DM with different mass function of lens taken into consideration. For a null search with $1000$ detected GW events of BBH, we find that the abundance of compact DM could be constrained to $\lesssim0.1\%$ in the mass range $\geq500~M_{\odot}$ at $68\%$ confidence level. In addition, if a GW event lensed by a compact DM object with $M_{\rm l}\in[100~M_{\odot},300~M_{\odot}]$ is detected in $100$ detected GW events of BBH, we can derive that the estimation of the abundance of compact DM is from $2.3\%$ to $25.2\%$ in this mass range with the Bayesian analysis.