Joint estimation of the cosmological model and the mass and redshift distributions of the binary black hole population with the Einstein Telescope

We investigate the capability of constraining the mass and redshift distributions of binary black hole systems jointly with the underlying cosmological model using one year of observations of the Einstein Telescope. To this aim, we fixed the underlying cosmological model to a flat $Λ$CDM model, then we considered the mass distribution given by a smoothed power law, and the redshift distributions given by the Madau-Dickinson model. We built mock catalogs with different SNR thresholds, and finally inferred astrophysical and cosmological parameters jointly adopting a hierarchical Bayesian framework. We found that as the SNR threshold decreases, the precision on the matter density parameter $Ω_{m,0}$ and the Hubble constant $H_0$, improves significantly due to the increased number of detectable events at high redshift. However, degeneracies between cosmological and astrophysical parameters exist and evolve with the SNR threshold. Finally, we showed that one year of observations will serve to reconstruct the mass distribution with its features. Conversely, the redshift distribution will be poorly constrained and will need more observations to improve.