Alexander J. Dittmann, Adam M. Dempsey, Hui Li

The accretion disks that power active galactic nuclei (AGN) are thought to house populations of stars and compact objects; after forming binaries these compact objects may merge, begetting gravitational waves such as those detected by LIGO and VIRGO. We present a comprehensive study of the early evolution of binaries within AGN disks as their orbits are influenced by the surrounding gas, focusing on eccentric and unequal-mass binaries. Nearly-equal-mass binaries behave similarly to their equal-mass counterparts: prograde binaries inspiral, albeit somewhat slowly, and have their eccentricities damped; retrograde binaries inspiral $\sim2-3$ times faster than their prograde counterparts, and those with near-equal masses are driven quickly towards near-unity eccentricities. However, the primaries in retrograde binaries with mass ratios of $m_2/m_1\lesssim0.4$ experience significantly weaker headwinds and retain substantial accretion disks that help damp binary eccentricities, slowing binary inspirals. Additionally, we find that while accretion drives prograde binaries towards equal masses thanks to the exchange of material between the primary and secondary accretion disks, retrograde binaries are driven slowly towards more extreme mass ratios. Prograde binaries, and generally those with low mass ratios, likely accrete for multiple $e$-folding timescales before merger. On the other hand, high-mass-ratio retrograde binaries may merge before accreting substantially, potentially approaching merger with detectable eccentricity. Future ground-based gravitational wave observatories, with their broader frequency coverage, should be particularly useful for studying these populations.