Abstract In the third-generation (3G) gravitational-wave (GW) detector era, GW multi-messenger observations for binary neutron star merger events can exert significant effects on exploring the cosmic expansion history. Extending a previous work, we explore the potential of 3G GW standard siren observations in cosmological parameter estimation by considering their associated electromagnetic (EM) counterparts, including γ -ray burst (GRB) coincidence observations by the Gravitational Wave High-energy Electromagnetic Counterpart All-sky Monitor and GW-triggered target-of-opportunity observations of kilonovae by different optical survey projects. During an assumed 10-year observation, we predict that the number of detectable GW-kilonova events is 4900 ∼ 4900 with redshifts below 0. 4 ∼ 0. 4 under the GW detector network and Large Synoptic Survey Telescope in the i band, which is more than three times that of GW-GRB detections. For the cosmological analysis, we find that with the inclusion of GW-kilonova detections, the constraints on cosmological parameters from GW-EM detections are significantly improved compared to those from GW-GRB detections. In particular, GW-EM detections can tightly constrain the Hubble constant with precision ranging from 0. 076\% 0. 076 % to 0. 034\% 0. 034 %. Moreover, GW multi-messenger observations can effectively break the cosmological parameter degeneracies generated by the typical EM observations, CMB+BAO+SN (CBS). The combination of CBS and GW-EM can tightly constrain the equation-of-state parameters of dark energy w in the w CDM model and w₀ w 0 in the w₀wₐ w 0 w a CDM model with precision of 0. 72\% 0. 72 % and 0. 99\% 0. 99 %, respectively, meeting the standard of precision cosmology. In conclusion, GW multi-messenger observations could play a crucial role in helping solve the Hubble tension and probing the fundamental nature of dark energy.
Han et al. (2026) studied this question.