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In the coming decades, the space-based gravitational-wave (GW) detectors suchas Taiji, TianQin, and LISA are expected to form a network capable of detectingmillihertz GWs emitted by the mergers of massive black hole binaries (MBHBs).In this work, we investigate the potential of GW standard sirens from theTaiji-TianQin-LISA network in constraining cosmological parameters. For theoptimistic scenario in which electromagnetic (EM) counterparts can be detected,we predict the number of detectable bright sirens based on three different MBHBpopulation models, i.e., pop III, Q3d, and Q3nod. Our results show that theTaiji-TianQin-LISA network alone could achieve a constraint precision of$0.9\%$ for the Hubble constant, meeting the standard of precision cosmology.Moreover, the Taiji-TianQin-LISA network could effectively break thecosmological parameter degeneracies generated by the CMB data, particularly inthe dynamical dark energy models. When combined with the CMB data, the jointCMB+Taiji-TianQin-LISA data offer $\sigma(w)=0.036$ in the $w$CDM model, whichis close to the latest constraint result obtained from the CMB+SN data. We alsoconsider a conservative scenario in which EM counterparts are not available.Due to the precise sky localizations of MBHBs by the Taiji-TianQin-LISAnetwork, the constraint precision of the Hubble constant is expected to reach$1.2\%$. In conclusion, the GW standard sirens from the Taiji-TianQin-LISAnetwork will play a critical role in helping solve the Hubble tension andshedding light on the nature of dark energy.

The Taiji-TianQin-LISA network: Precisely measuring the Hubble constant using both bright and dark sirens