Three-band dark-siren cosmology with intermediate mass black hole binaries: Synergy of Taiji, LGWA, and the Einstein Telescope

Gravitational-wave (GW) dark sirens provide an independent probe of the cosmic expansion history. Their cosmological constraining power, however, depends critically on precise luminosity-distance measurements and sky localizations for cross-matching with galaxy catalogs. Multiband GW observations can track GW events across different frequency bands and thus improve both. Motivated by this, we forecast the cosmological potential of intermediate-mass black hole binaries (IMBHBs) observed by a three-band GW detector network composed of Taiji (TJ), the Lunar Gravitational-wave Antenna (LGWA), and the Einstein Telescope (ET). We simulate detectable IMBHB populations and analyze them with a hierarchical Bayesian dark-siren framework that includes galaxy-catalog completeness and redshift uncertainties. We find that the TJ-LGWA-ET network outperforms all two-detector configurations considered here. In the $\mathrm{\ensuremath{\Lambda}}$ cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model, it constrains the Hubble constant and matter density to $\ensuremath{\sim}0.12%$ and $\ensuremath{\sim}0.6%$, respectively. In the $w\mathrm{CDM}$ model, a 4-year dark-siren sample alone constrains the dark-energy equation-of-state parameter $w$ to $\ensuremath{\sim}2.7%$. Adding baryon acoustic oscillation (BAO) and Type Ia supernova (SNe Ia) data improves the $w$ constraint to $\ensuremath{\sim}2.1%$, slightly better than that from the current $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SNe}$ Ia combination. We also show that the final constraints remain sensitive to IMBHB population assumptions and galaxy-catalog limitations, which highlights the need for deep galaxy surveys with precise redshift measurements.