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.
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