  Gravitational-wave astronomy provides a unique new way to study the expansion
history of the Universe. In this work, we investigate the impact future
gravitational-wave observatories will have on cosmology. Third-generation
observatories like the Einstein Telescope and Cosmic Explorer will be sensitive
to essentially all of the binary black hole coalescence events in the Universe.
Recent work by \cite{farr2019future} points out that features in the
stellar-mass black hole population break the mass-redshift degeneracy,
facilitating precise determination of the Hubble parameter without
electromagnetic counterparts or host galaxy catalogues. Using a hierarchical
Bayesian inference model, we show that with one year of observations by the
Einstein Telescope, the Hubble constant will be measured to $\lesssim 1\%$. We
also show that this method can be used to perform Bayesian model selection
between cosmological models. As an illustrative example, we find that a
decisive statement can be made comparing the $\Lambda$CDM and RHCT cosmological
models using two weeks of data from the Einstein Telescope.
