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Gravitational waves (GWs) from compact binary coalescences encode theabsolute luminosity distances of GW sources. Once the redshifts of GW sourcesare known, one can use the distance-redshift relation to constrain cosmologicalparameters. One way to obtain the redshifts is to localize GW sources by GWobservations and then use galaxy catalogs to determine redshifts from astatistical analysis of redshift information of the potential host galaxies,commonly referred to as the dark siren method. The third-generation (3G) GWdetectors are planned to work in the 2030s and will observe numerous compactbinary coalescences. Using these GW events as dark sirens requires high-qualitygalaxy catalogs from future sky survey projects. The China Space StationTelescope (CSST) will be launched in 2024 and will observe billions of galaxieswithin a 17500 deg$^2$ survey area with redshift up to $z\sim 4$, providingphotometric and spectroscopic galaxy catalogs. In this work, we simulate theCSST galaxy catalogs and the 5-year GW data from the 3G GW detectors andcombine them to infer the Hubble constant ($H_0$). Our results show that themeasurement precision of $H_0$ could reach the sub-percent level, meeting thestandard of precision cosmology. We conclude that the synergy between CSST andthe 3G GW detectors is of great significance in measuring the Hubble constant.

Synergy between CSST galaxy survey and gravitational-wave observation: Inferring the Hubble constant from dark standard sirens