We present a novel self-consistent theoretical framework to characterize the formation, evolution, and merger sites of dynamically formed black hole binaries, with a focus on explaining the most massive events observed by the LIGO-Virgo-KAGRA Collaboration. Our approach couples the galaxy formation model with cluster population synthesis codes to trace the cosmic evolution of globular clusters simultaneously with mergers of massive black holes. Our reference model, which includes prescriptions for both cluster formation and disruption depending on properties of specific galaxies, accurately reproduces the observed age-mass distribution of the Milky Way's globular clusters. We find that approximately 30% of the globular clusters observed in our galaxy's halo may have originated from satellite galaxies of the Milky Way. We confirm that hierarchical black hole mergers provide a significant contribution to the formation of black holes in and above the pair-instability mass gap. However, quantifying their contribution is challenging, as different population synthesis codes yield divergent results in terms of the black hole mass function and merger rates. Furthermore, we characterize the host galaxies where massive black holes form in terms of their dark matter, stellar mass, and metallicity. Ultimately, we demonstrate that the merger and birth rate densities of binary black holes increase with redshift until = 5. This cosmic evolution is a crucial signature with significant implications for future detectors such as LISA, the Einstein Telescope, and Cosmic Explorer, which will be capable of probing the high-redshift Universe. GAMESH z
Angeloni et al. (Tue,) studied this question.