Information about the mass spectrum of compact stars can be used to infer cosmological parameters from gravitational waves (GW) in the absence of redshift measurements obtained from electromagnetic (EM) observations. This method will be fundamental in measuring and testing cosmology with GWs for current and future ground-based GW detectors where the majority part of sources are detected without an associated EM counterpart.
In this proceeding, we will discuss the prospects and limitations of this approach for studying cosmology. We will show that, even when assuming GW detectors with current sensitivities, the determination of the Hubble constant is strongly degenerate with the maximum mass for black hole production.
We will discuss how assuming wrong models for the underlying population of black hole events can bias the Hubble constant estimate up to 40\%.