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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 andcosmology. If compact dark matter (DM) objects e.g. primordial black holes,contribute a significant fraction of dark matter at wide mass range, they willcause microlensing in the GW signals with long wavelengths that are distinctfrom the lensing effects of electromagnetic signals from astrophysical objects.In this paper, we apply the lensing effect of GW from BBH to derive constraintson the abundance of compact DM for the Cosmic Explorer, a third-generationground-based GW detector. We firstly consider two channels of formation of BBHthat contribute to low and high redshift GW sources, including theastrophysical origin BBH scenario, and the primordial origin BBH scenario.Secondly, comparing with the method of optical depth, we use the Bayesiananalysis to derive constraints on the abundance of compact DM with differentmass 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 beconstrained 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 GWevents of BBH, we can derive that the estimation of the abundance of compact DMis from $2.3\%$ to $25.2\%$ in this mass range with the Bayesian analysis.

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