Synergy between CSST and third-generation gravitational-wave detectors: Inferring cosmological parameters using cross-correlation of dark sirens and galaxies

Gravitational-wave (GW) events are generally believed to originate in galaxies and can thus serve, like galaxies, as tracers of the universe's large-scale structure. In GW observations, waveform analysis provides direct measurements of luminosity distances; however, without relying on a specific cosmological model, the redshifts of GW sources cannot be determined due to the mass-redshift degeneracy. By cross-correlating GW events with galaxies, one can establish a correspondence between luminosity distance and redshift shells, enabling cosmological inference. In this work, we explore the scientific potential of cross-correlating GW sources detected by third-generation (3G) ground-based GW detectors with the photometric redshift survey of the China Space Station Survey Telescope (CSST). We find that the constraint precisions of the Hubble constant and the matter density parameter can reach $1.04\%$ and $2.04\%$, respectively. Additionally, we have also constrained the precision of the GW clustering bias parameter. These results highlight the significant potential of the synergy between CSST and 3G ground-based GW detectors in constraining cosmological models and probing GW source formation channels using cross-correlation of dark sirens and galaxies.