Calibrating systematic errors in the distance determination with the
  luminosity-distance space large scale structure of dark sirens and its
  potential applications
  The cosmological luminosity-distance can be measured from gravitational wave
(GW) standard sirens, free of astronomical distance ladders and the associated
systematics. However, it may still contain systematics arising from various
astrophysical, cosmological and experimental sources. With the large amount of
dark standard sirens of upcoming third generation GW experiments, such
potential systematic bias can be diagnosed and corrected by statistical tools
of the large scale structure of the universe. We estimate that, by
cross-correlating the dark siren luminosity-distance space distribution and
galaxy redshift space distribution, multiplicative error $m$ in the luminosity
distance measurement can be constrained with $1\sigma$ uncertainty
$\sigma_m\sim 0.1$. This is already able to distinguish some binary black hole
origin scenarios unambiguously. Significantly better constraints and therefore
more applications may be achieved by more advanced GW experiments.
