Multiband gravitational wave cosmography with dark sirens

Gravitational waves might help resolve the tension between early and late Universe measurements of the Hubble constant, and this possibility can be enhanced with a gravitational wave detector in the decihertz band as we will demonstrate in this study. Such a detector is particularly suitable for the multiband observation of stellar-mass black hole binaries between space and ground, which would significantly improve the source localization accuracy thanks to a long baseline for timing triangulation, hence promoting the "dark siren" cosmology. Proposed decihertz concepts include Decihertz Interferometer Gravitational Wave Observatory (DECIGO)/B-DECIGO, TianGO, and others. We consider here the prospects of multiband observation of dark siren binaries with a variety of network configurations. We find that a multiband observation can uniquely identify a black hole binary to a single galaxy to a cosmological distance, and thus a dark siren behaves as if it had an electromagnetic counterpart. Considering only fully localized dark sirens, we use a Fisher matrix approach to estimate the error in the Hubble constant and matter density parameter. We find that a decihertz detector substantially improves our ability to measure cosmological parameters because it enables host galaxies to be identified out to a larger distance without the systematics from statistical techniques based on comparing the population distribution.