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

Abstract: 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. It has been recently shown that a mismodeling of the BBH mass spectrum is very likely to introduce a bias in the determination of the Hubble constant. To tackle this issue, we develop a BBH population model based on Normalizing Flows, trained on synthetic BBH catalogs generated from astrophysical prescriptions, including binaries formed through both isolated stellar evolution and dynamical environments. We validate this approach with a mock BBH dataset, demonstrating that the Normalizing Flow framework faithfully recovers the true distribution and eliminates systematic biases in the Hubble constant inference. By using this model on GWTC-4.0 data, we obtain $H_0 = 71.62^{+4.04}_{-4.00}\; km \; s^{-1} Mpc^{-1}$ at 68.3% credible interval. Assuming the astrophysical prescriptions present in B-POP, we also show that the determination of $H_0$ is degenerate with the fraction of binaries born in the dynamical and isolated formation channel, with a Planck cosmology favouring $\sim 35\%$ binaries formed in the dynamical environment while a SH0ES cosmology favouring a value of $\sim 25\%$.