Cosmic evolution of stellar-mass black hole merger rate in active galactic nuclei

Binary black hole mergers encode information about their environment and the astrophysical processes that led to their formation. Measuring the redshift dependence of their merger rate will help probe the formation and evolution of galaxies and the evolution of the star formation rate. Here we compute the cosmic evolution of the merger rate for stellar-mass binaries in the disks of active galactic nuclei (AGNs). We focus on recent evolution out to redshift z = 2, covering the accessible range of current Earth-based gravitational-wave observatories. On this scale, the AGN population density is the main contributor to redshift dependence. We find that the AGN-assisted merger rate varies by less than a factor of two in the range 0 < z ≤ 2, comparable to the expected level of evolution for globular clusters, but much smaller than the order-of-magnitude evolution for field binaries.