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During the first three observing runs of the Advanced gravitational-wavedetector network, the LIGO/Virgo collaboration detected several black holebinary (BHBH) mergers. As the population of detected BHBH mergers grows, itwill become possible to constrain different channels for their formation. Herewe consider the chemically homogeneous evolution (CHE) channel in closebinaries, by performing population synthesis simulations that combine realisticbinary models with detailed cosmological calculations of the chemical andstar-formation history of the Universe. This allows us to constrain populationproperties, as well as cosmological and aLIGO/aVirgo detection rates of BHBHmergers formed through this pathway. We predict a BHBH merger rate at redshiftzero of $5.8 \, \textrm{Gpc}^{-3} \textrm{yr}^{-1}$ through the CHE channel, tobe compared with aLIGO/aVirgo's measured rate of ${53.2}_{-28.2}^{+55.8} \,\text{Gpc}^{-3} \text{yr}^{-1}$, and find that eventual merger systems have BHmasses in the range $17 - 43 \, \textrm{M}_{\odot}$ below the pair-instabilitysupernova (PISN) gap, and $>124 \, \textrm{M}_{\odot}$ above the PISN gap. Weinvestigate effects of momentum kicks during black hole formation, andcalculate cosmological and magnitude limited PISN rates. We also study theeffects of high-redshift deviations in the star formation rate. We find thatmomentum kicks tend to increase delay times of BHBH systems, and our magnitudelimited PISN rate estimates indicate that current deep surveys should be ableto detect such events. Lastly, we find that our cosmological merger rateestimates change by at most $\sim 8\%$ for mild deviations of the starformation rate in the early Universe, and by up to $\sim 40\%$ for extremedeviations.

Cosmic Rates of Black Hole Mergers and Pair-Instability Supernovae from Chemically Homogeneous Binary Evolution