  In the coming decades, the space-based gravitational-wave (GW) detectors such
as Taiji, TianQin, and LISA are expected to form a network capable of detecting
millihertz GWs emitted by the mergers of massive black hole binaries (MBHBs).
In this work, we investigate the potential of GW standard sirens from the
Taiji-TianQin-LISA network in constraining cosmological parameters. For the
optimistic scenario in which electromagnetic (EM) counterparts can be detected,
we predict the number of detectable bright sirens based on three different MBHB
population models, i.e., pop III, Q3d, and Q3nod. Our results show that the
Taiji-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 the
cosmological parameter degeneracies generated by the CMB data, particularly in
the dynamical dark energy models. When combined with the CMB data, the joint
CMB+Taiji-TianQin-LISA data offer $\sigma(w)=0.036$ in the $w$CDM model, which
is close to the latest constraint result obtained from the CMB+SN data. We also
consider a conservative scenario in which EM counterparts are not available.
Due to the precise sky localizations of MBHBs by the Taiji-TianQin-LISA
network, the constraint precision of the Hubble constant is expected to reach
$1.2\%$. In conclusion, the GW standard sirens from the Taiji-TianQin-LISA
network will play a critical role in helping solve the Hubble tension and
shedding light on the nature of dark energy.
