Gravitational-wave observations are rapidly transitioning from individual detections to population studies. Interpreting these observations requires robust predictions for binary black hole merger rates and mass spectra plus a consistent link between stellar progenitors and compact object populations across cosmic time.
In this talk, I present a new data-driven framework for cosmic star formation combined with advanced population synthesis simulations to construct binary black hole merger rates and mass spectra models necessary for hierarchical inference. I will show how this approach connects progenitor physics to observable black hole populations, highlighting both what these models can reliably predict and where they fall short.
Finally, I will present forecasts for the Einstein Telescope, including expected detection rates and what we can learn about cosmological parameters and astrophysical prescriptions. I will then use this framework to address three open questions, already relevant for the Ligo Virgo Kagra collaboration and crucial for the high-redshift population accessible to the Einstein Telescope: whether the primary and secondary black hole masses follow the same distribution; whether stellar mergers in young star clusters can produce intermediate-mass black holes; and whether simulation-based inference can enable more efficient population analyses.