Abstract The Hubble constant H0 tension is a well-known issue of the cosmology This problem stems from the inconsistency between the value of H0 fitted after the cosmological model is constrained by t

The Hubble constant (H0) tension is a known problem in cosmology that arises from a discrepancy between the value of H0 obtained from the cosmic microwave background (CMB) anisotropies and other astrophysical data and the direct measurement of H0 using the cosmic distance ladder. To resolve this tension, we need new cosmological probes that can provide an independent measurement of H0. The gravitational-wave (GW) dark standard siren is one such probe. In this presentation, we discuss our recent work that uses a mock galaxy catalog from the China Space Station Telescope (CSST) combined with simulated dark standard siren data from the next generation of ground-based GW detectors to constrain H0. Our results show that the synergy between CSST and GW data can provide an accurate measurement of H0 with an error of less than 1%, providing a possible resolution to the H0 tension. Our work highlights the potential of combining different cosmological probes to address fundamental questions in cosmology