Hierarchical Black Hole Mergers in AGN Disks: Tracing Massive Black Hole Growth Across Cosmic Time

The dense and gaseous environments of active galactic nuclei (AGNs) can catalyze repeated mergers of stellar-mass black holes (BHs), potentially explaining the high-mass tail of binary black hole (BBH) mergers observed by LIGO-Virgo-KAGRA (LVK). We present a semi-analytical population synthesis framework that captures key physical processes in AGN disks, including gas capture, migration, binary pair-up, gas hardening, and dynamical binary-single interactions. Our simulations show that AGN disks can produce hierarchical mergers, especially near migration traps, and may contribute to the high-mass, high-spin BBH population. This work opens prospects for constraining both the AGN channel and supermassive black hole growth with future gravitational-wave detections.