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 quantity for diagnostics is their distribution with respect to the large scale structures of the universe, as encoded, for instance, in their (linear) biases. We discuss the perspectives of inferring these quantities via the cross-correlation of galaxy catalogs with mock GW ones, using both existing and forthcoming galaxy catalogs and using realistic Monte Carlo simulations of GW events. We find that the bias should be marginally detectable for a 10-year data taking of current generation detectors at design sensitivity, at least for binary neutron star mergers. The forthcoming five detector network would allow for a firmer detection of this signal and, in combination with future cosmological surveys, would also permit the detection of the coalescing black hole bias. Such a measurement may also 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, which will allow one to perform precision studies of the coalescing black holes bias and attain rather advanced model discrimination capabilities, at a few percent level.