Cross-correlating galaxy catalogs and gravitational waves: a tomographic
  approach
  Unveiling the origin of the coalescing binaries detected via gravitational
waves (GW) is challenging, notably if no multi-wavelength counterpart is
detected. One important diagnostic tool is the coalescing binary distribution
with respect to the large scale structures (LSS) of the universe, which we
quantify via the cross-correlation of galaxy catalogs with GW ones. By using
both existing and forthcoming galaxy catalogs and using realistic Monte Carlo
simulations of GW events, we find that the cross-correlation signal should be
marginally detectable in a 10-year data taking of advanced LIGO-Virgo detectors
at design sensitivity, at least for binary neutron star mergers. The expected
addition of KAGRA and LIGO-India to the GW detector network would allow for a
firmer detection of this signal and, in combination with future cosmological
surveys, would also permit the detection of cross-correlation for coalescing
black holes. Such a measurement may unveil, for instance, a primordial origin
of coalescing black holes. To attain this goal, we find that it is crucial to
adopt a tomographic approach and to reach a sufficiently accurate localization
of GW events. The depth of forthcoming surveys will be fully exploited by third
generation GW detectors such as the Einstein Telescope or the Cosmic Explorer,
which will allow one to perform precision studies of the coalescing black hole
LSS distribution and attain rather advanced model discrimination capabilities.
