The lure of sirens: joint distance and velocity measurements with third-generation detectors

The next generation of detectors will detect gravitational waves from binary neutron stars at cosmological distances, for which around a 1000 electromagnetic follow-ups may be observed per year. So far, most work devoted to the expected cosmological impact of these standard sirens employed them only as distance indicators. Only recently their use as tracers of clustering, similar to what already proposed for supernovae, has been studied. Focusing on the expected specifications of the Einstein Telescope (ET), we forecast here the performance on cosmological parameters of future standard sirens as both distance and density indicators, with emphasis on the linear perturbation growth index and on spatial curvature. We improve upon previous studies in a number of ways: a more detailed analysis of available telescope time, the inclusion of more cosmological and nuisance parameters, the Alcock-Paczynski correction, the use of sirens also as both velocity and density tracers, and a more accurate estimation of the distance posterior. We find that the analysis of the clustering of sirens improves the constraints on H0 by 30 per cent and on Ωk0 by over an order of magnitude, with respect to their use merely as distance indicators. With 5 yr of joint ET and Rubin Observatory follow-ups we could reach precision of 0.1 km s-1 Mpc-1 in H0 and 0.02 in Ωk0 using only data in the range 0 < z < 0.5. We also find that the use of sirens as tracers of density, and not only velocity, yields good improvements on the growth of structure constraints.