How can gravitational-wave standard sirens and 21 cm intensity mapping jointly provide a precise late-universe cosmological probe?

In the next decades, the gravitational-wave (GW) standard siren observations and the neutral hydrogen 21-cm intensity mapping (IM) surveys, as two promising cosmological probes, will play an important role in precisely measuring cosmological parameters. In this work, we make a forecast for cosmological parameter estimation with the synergy between the GW standard siren observations and the 21-cm IM surveys. We choose the Einstein Telescope (ET) and the Taiji observatory as the representatives of the GW detection projects and choose the Square Kilometre Array (SKA) phase I mid-frequency array as the representative of the 21-cm IM experiments. In the simulation of the 21-cm IM data, we assume perfect foreground removal and calibration. We find that the synergy of the GW standard siren observations and the 21-cm IM survey could break the cosmological parameter degeneracies. The joint ET+Taiji+SKA data give (H₀) =0. 28\ km\ s^{-1\ Mpc^-1} in the CDM model, (w) =0. 028 in the wCDM model, which are better than the results of Planck+BAO+SNe, and (w₀) =0. 077 and (wₐ) =0. 295 in the CPL model, which are comparable with the results of Planck+BAO+SNe. In the CDM model, the constraint precision of H₀ and ₌ is less than or rather close to 1%, indicating that the magnificent prospects for precision cosmology with these two promising cosmological probes are worth expecting.