  After the nearly hundred gravitational-wave detections reported by the
LIGO-Virgo-KAGRA Collaboration, the question of the cosmological origin of
merging binary black holes (BBHs) remains open. The two main formation channels
generally considered are from isolated field binaries or via dynamical assembly
in dense star clusters. Here, we focus on understanding the dynamical formation
of merging BBHs within massive clusters in galaxies of different masses. To
this end, we apply a new framework to consistently model the formation and
evolution of massive star clusters in zoom-in cosmological simulations of
galaxies. Each simulation, taken from the FIRE project, provides a realistic
star formation environment with a unique star formation history and hosts
realistic giant molecular clouds that constitute the birthplace of star
clusters. Combined with the code for star cluster evolution CMC, we are able to
produce populations of dynamically formed merging BBHs across cosmic time in
different environments. As the most massive star clusters preferentially form
in dense massive clouds of gas, we find that, despite their low metallicities
favourable to the creation of black holes, low-mass galaxies contain few
massive clusters and therefore have a limited contribution to the global
production of dynamically formed merging BBHs. Furthermore, we find that
massive clusters can host hierarchical BBH mergers with clear identifiable
physical properties. Looking at the evolution of the BBH merger rate in
different galaxies, we find strong correlations between BBH mergers and the
most extreme episodes of star formation. Finally, we discuss the implications
for future LIGO-Virgo-KAGRA gravitational wave observations.
