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.
