SIMBAD references

We present a comprehensive forecast for cosmological constraints using the joint observation of the cosmic shear signal from the Chinese Space Station Survey Telescope (CSST) and the clustering signal from the next-generation gravitational wave (GW) detector networks, e.g., Einstein Telescope and Cosmic Explorer. By leveraging the angular clustering of astrophysical gravitational wave sources (AGWS) from the third-generation detectors and CSST's weak lensing surveys, we develop a theoretical framework to compute auto- and cross-angular power spectra of AGWS clustering, cosmic shear, and their cross correlation. Mock data sets are generated by considering the detector-specific selection functions, uncertainties in luminosity distance, and weak lensing systematics. We employ the Markov Chain Monte Carlo methods to constrain the ΛCDM cosmological parameters, AGWS bias parameters, and star formation rate parameters under three detector configurations. Our results demonstrate that the joint observation can achieve sub-5% precision on H₀ (2.19%) and w (5.7%). In addition, the AGWS clustering bias parameters can be constrained to a precision of 4%-5%, enabling the differentiation between stellar-origin compact binaries and primordial black hole scenarios. This multimessenger approach can also be helpful to resolve mass-redshift degeneracies in the dark siren methods, providing independent validation for Hubble tension. Our work indicates that the joint observation of the third-generation GW detectors and the CSST can be a powerful probe of large-scale structure and the cosmic expansion history.