Spectral siren cosmology from gravitational-wave observations in GWTC-4.0

Gravitational wave standard sirens offer a promising avenue for cosmological inference, particularly in measuring the expansion history of the universe. Traditionally, bright sirens require an electromagnetic counterpart to determine the redshift of the emission source while dark sirens rely on the presence of complete galaxy catalogs over large sky regions. Spectral sirens, using GW data alone, can circumvent these limitations by leveraging features in the mass distribution of compact binaries. With the recent release of the Gravitational-Wave Transient Catalog 4 (GWTC-4.0), the number of significant binary black hole (BBH) merger candidates has increased to 153, enabling more robust population studies and cosmological constraints. This work builds upon previous spectral siren analyses by analyzing the latest BBH observations with parametric and non-parametric models. In particular, we consider a parametric approach using the Powerlaw + Peak and Broken Powerlaw + 2 Peaks models as well as a more flexible non-parametric model based on Gaussian processes. We find broad consistency in the inferred Hubble constant $H_0$ constraints across models. Our most constraining result is from the Gaussian Process model, which, combined with the GW170817 bright siren measurement, results in $H_0 = 69^{+7}_{-6} \ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, a 10% precision measurement. For the Powerlaw + Peak and Broken Powerlaw + 2 Peaks we find fractional uncertainties of 17% and 13% respectively.