Enhancing dark siren cosmology through multi-band gravitational wave synergetic observations

Multi-band gravitational-wave (GW) standard siren observations are poised to herald a new era in the study of cosmic evolution. These observations offer higher signal-to-noise ratios and improved localizations compared to those achieved with single-band GW detection, which are crucial for the cosmological applications of dark sirens. In this work, we explore the role multi-band GW synergetic observations will play in measuring cosmological parameters, particularly in comparison with single GW observatory data. We used mock multi-band dark siren data from third-generation GW detectors and the baseline Decihertz Interferometer Gravitational-Wave Observatory to infer cosmological parameters. Our analysis shows that multi-band GW observations significantly improve sky localization accuracy by two to three orders of magnitude over single-band observations, although their impact on luminosity distance error remains limited. This results in a substantial improvement in the constraints on matter density and the Hubble constant, enhancing their constraint precision by $60\%$-$90\%$ and $52\%$-$85\%$, respectively. We conclude that the significant potential of multi-band GW synergistic observations for detecting GW signals and resolving the Hubble tension is highly promising and warrants anticipation.