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 $\sigma(H_0)=0.28\ {\rm km\ s^{-1}\ Mpc^{-1}}$ in the $\Lambda$CDM model, $\sigma(w)=0.028$ in the $w$CDM model, which are better than the results of $Planck$+BAO+SNe, and $\sigma(w_0)=0.077$ and $\sigma(w_a)=0.295$ in the CPL model, which are comparable with the results of $Planck$+BAO+SNe. In the $\Lambda$CDM model, the constraint precision of $H_0$ and $\Omega_{\rm m}$ 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.