Hubble parameter estimation via dark sirens with the lisa-taiji network

The measurement of the Hubble parameter ($H_0$) has arrived at a crossroads. The values of $H_0$ inferred from the late-time observations are systematically higher (about $10\%$) than those from the early-time measurements. To come to a robust conclusion, independent probes with accuracy at percent levels are crucial. Without relying on any astrophysical modeling, gravitational waves (GWs) from compact binary coalescence (CBC) events open a completely novel observational window for $H_0$ determination. Depends on whether being associated with electromagnetic (EM) counterparts or not, GW events can be categorized into standard sirens and dark sirens. The former demand fairly good synergies, which are extremely challenging for high redshift CBC events, while the latter, which do not rely on transient measurements, ask for a precise sky localization to reduce the number of possible host galaxies. The future space-based GW observatory network, such as the LISA-Taiji network, will be able to localize the CBC events with unprecedented accuracy. Here we show that within $5$ years operation time, the LISA-Taiji network is able to constrain the Hubble parameter within $1\%$ accuracy, and possibly beats the scatters down to $0.5\%$ or even better.