Multi-band Gravitational Wave Cosmography with Dark Sirens*

Gravitational waves might help resolve the tension between early and late Universe measurements of the Hubble constant. Recently, there has been enhanced interest in the possibility of gravitational wave detectors in the deci-hertz band which bridges the gap between LISA and ground-based detectors. Such a detector is particularly suitable for the multi-band 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 deci-hertz concepts include DECIGO/B-DECIGO, TianGO, and others. We consider here the multi-band observation of dark-siren binaries using TianGO at 0.1-10 Hz and a network of LIGO Voyagers at 10-100 Hz. We find that this configuration can uniquely identify a black-hole binary to a single galaxy, and thus a dark siren behaves as if it had an electromagnetic counterpart. Considering only fully localized dark sirens, we use a Fisher matrix to estimate the error in the Hubble constant and matter density parameter. We find that a deci-hertz detector substantially improves our ability to measure cosmological parameters because it enables galaxies to be identified out to a larger distance without the systematics from statistical techniques.