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The cosmological luminosity-distance can be measured from gravitational wave(GW) standard sirens, free of astronomical distance ladders and the associatedsystematics. However, it may still contain systematics arising from variousastrophysical, cosmological and experimental sources. With the large amount ofdark standard sirens of upcoming third generation GW experiments, suchpotential systematic bias can be diagnosed and corrected by statistical toolsof the large scale structure of the universe. We estimate that, bycross-correlating the dark siren luminosity-distance space distribution andgalaxy redshift space distribution, multiplicative error $m$ in the luminositydistance measurement can be constrained with $1\sigma$ uncertainty$\sigma_m\sim 0.1$. This is already able to distinguish some binary black holeorigin scenarios unambiguously. Significantly better constraints and thereforemore applications may be achieved by more advanced GW experiments.

monthly notices of the royal astronomical society

Calibrating systematic errors in the distance determination with the  luminosity-distance space large scale structure of dark sirens and its  potential applications