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Knowledge of the shape of the mass spectrum of compact objects can be used tohelp break the degeneracy between the mass and redshift of the gravitationalwave (GW) sources, and thus can be used to infer cosmological parameters in theabsence of redshift measurements obtained from electromagnetic observations. Inthis paper, we study extensively different aspects of this approach, includingits computational limits and achievable accuracy. We focus on ground-baseddetectors with current and future sensitivities, we first perform the analysisof an extensive set of simulated data with a hierarchical Bayesian schemeinferring population and cosmological parameters. We consider a populationmodel (power-law plus Gaussian) which exhibits characteristic scales (extremesof the mass spectrum, presence of an accumulation point) that allows anindirect estimate of the source redshift. Our analysis of this cataloghighlights and quantifies the tight interplay between source population andcosmological parameters, as well as the influence of initial assumptions(whether formulated on the source or cosmological parameters). We then validateour results by an "end-to-end" analysis using simulated GW data and posteriorsamples generated from Bayesian samplers used for GW parameter estimation, thusmirroring the analysis chain used for observational data for the first time inliterature. Our results then lead us to re-examine the estimation of $H_0$obtained with GWTC-1, and we show explicitly how population assumptions impactthe final $H_0$ result. Our results underline the importance of inferringpopulation and cosmological parameters jointly (and not separately as is oftenassumed). The only exception, as we discuss, is if an electromagneticcounterpart was to be observed for all the BBH events: then the populationassumptions have less impact on the estimation of cosmological parameters.

Cosmology in the dark: On the importance of source population models for gravitational-wave cosmology