Calibrating spectral siren cosmology with synthetic catalogs of binary black hole mergers

Binary black hole (BBH) mergers detected through Gravitational Waves (GWs) are a promising probe for the cosmic expansion. These sources are standard sirens for which we can directly measure the luminosity distance, but their redshift is degenerate with the determination of their source masses. In analogy to standard candles, the redshift of standard sirens can be obtained using a calibration based on the source mass spectrum, but without the need for a cosmological ladder. The modelling of the BBH mass spectrum is crucial for GW cosmology. In this paper, we propose a new pipeline based on Normalizing Flows to calibrate population models on synthetic BBH catalogs generated from astrophysical prescriptions. Although these models are less flexible than the current parametric models used in the literature, they have the advantage of directly capturing the correlations between BBH mass and redshift and provide a direct link between different formation channels and cosmological parameter inference. We discuss potential applications and limitations of this method using the B-POP code to generate a mock catalog that contains BBH formed by isolated stellar binaries and in dense stellar environments via dynamical interactions. Using this methodology, we show that B-POP provides a good fit for the mass and redshift distributions of the GW events in GWTC-4.0 data for a flat Λ CDM cosmology with H 0 about 70 km/s/Mpc and Ω m=0.308. We also find a correlation between H 0 and the fraction of binaries produced by the dynamical and isolated formation channels arising from the fact that dynamically formed binaries populate the higher side of the mass spectrum.