Constraining the Hubble constant to a precision of about 1% using multi-band dark standard siren detections

Gravitational wave signal from the inspirai of stellar-mass binary black hole can be used as standard sirens to perform cosmological inference. This inspirai covers a wide range of frequency bands, from the millihertz band to the audio-band, allowing for detections by both space-borne and ground-based gravitational wave detectors. In this work, we conduct a comprehensive study on the ability to constrain the Hubble constant using the dark standard sirens, or gravitational wave events that lack electromagnetic counterparts. To acquire the redshift information, we weight the galaxies within the localization error box with photometric information from several bands and use them as a proxy for the binary black hole redshift. We discover that TianQin is expected to constrain the Hubble constant to a precision of roughly 30% through detections of 10 gravitational wave events; in the most optimistic case, the Hubble constant can be constrained to a precision of