A Flexible Mass Function for Binary Black Holes: Improving Cosmological Inference with Standard Sirens

Gravitational waves (GWs) from compact binary coalescences are a novel cosmological probe, opening a new window on the Universe. They act as standard sirens, providing an independent measurement of the luminosity distance, without distance-ladder assumptions. However, to fully exploit the cosmological potential of the growing number of standard sirens, a more accurate characterization of the underlying source population has become essential. In this Thesis, we develop and implement a semi-parametric model of the BBH primary mass function in a Bayesian framework, providing a flexible alternative to fully parametric approaches. The model combines a power-law baseline with a spline component. To maximize its versatility, we introduce different knot placement strategies, from logarithmic spacing to a novel data-driven approach. We then integrate this model into the CHIMERA code and extensively test and validate it. Using mock GW data, we assess its performance in a LIGO-Virgo-KAGRA Observing Run 5 scenario, showing robust mass function reconstruction for dark and spectral sirens configurations. Finally, we present the first application of this model to real data, analyzing 137 BBH events from the recently released GWTC-4 catalog as spectral sirens. We find that the model reconstructs the BBH mass distribution more robustly than standard parametric ones, as verified by Bayesian diagnostics. Crucially, we show that this improved reconstruction translates into tighter cosmological constraints, leading to a 12% improvement in the inference of the Hubble constant. We also investigate the impact of knot placement, demonstrating that poor choices can introduce significant biases in H0. This work shows that improved BBH mass modeling is crucial for maximizing the scientific return of GWs and provides valuable insights for the analysis of future standard sirens. These results have contributed to the submitted work Tagliazucchi M., Moresco M., Borghi N., Ciapetti C. (2026).