  Clustering measurements of Gravitational Wave (GW) mergers in Luminosity
Distance Space can be used in the future as a powerful tool for Cosmology. We
consider tomographic measurements of the Angular Power Spectrum of mergers both
in an Einstein Telescope-like detector network and in some more advanced
scenarios (more sources, better distance measurements, better sky
localization). We produce Fisher forecasts for both cosmological (matter and
dark energy) and merger bias parameters. Our fiducial model for the number
distribution and bias of GW events is based on results from hydrodynamical
simulations. The cosmological parameter forecasts with Einstein Telescope are
less powerful than those achievable in the near future via galaxy clustering
observations with, e.g., Euclid. However, in the more advanced scenarios we see
significant improvements. Moreover, we show that bias can be detected at high
statistical significance. Regardless of the specific constraining power of
different experiments, many aspects make this type of analysis interesting
anyway. For example, compact binary mergers detected by Einstein Telescope will
extend up to very high redshifts. Furthermore, Luminosity Distance Space
Distortions in the GW analysis have a different structure with respect to
Redshift-Space Distortions in galaxy catalogues. Finally, measurements of the
bias of GW mergers can provide useful insight into their physical nature and
properties.
