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

In the third-generation (3G) gravitational-wave (GW) detector era, the multi-messenger GW observation for binary neutron star (BNS) merger events can exert great impacts on exploring the cosmic expansion history. In this work, we comprehensively explore the potential of 3G GW standard siren observations in cosmological parameter estimations by considering the 3G GW detectors and the future short $\gamma$-ray burst (GRB) detector THESEUS-like telescope joint observations. Based on the 10-year observation of different detection strategies, we predict that the numbers of detectable GW-GRB events are 277-685 with the redshifts $z<4$ and the inclination angles $\iota