A comprehensive forecast for cosmological parameter estimation using joint observations of gravitational waves and short $$\gamma $$ γ -ray bursts

Abstract In the third-generation (3G) gravitational-wave (GW) detector era, multi-messenger GW observation for binary neutron star (BNS) merger events can exert great impacts on exploring cosmic expansion history. In this work, we comprehensively explore the potential of 3G GW standard siren observations in cosmological parameter estimations by considering 3G GW detectors and the future short $$\gamma $$ γ -ray burst (GRB) detector THESEUS-like telescope joint observations. Based on a 10-year observation of different detection strategies, we predict that the numbers of detectable GW-GRB events are 334–674 with the redshifts $$z