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The advent of gravitational-wave astronomy is now allowing for the study ofcompact binary merger demographics throughout the Universe. This informationcan be leveraged as tools for understanding massive stars, their environments,and their evolution. One active question is the nature of compact binaryformation: the environmental and chemical conditions required for black holebirth and the time delays experienced by binaries before they merge.Gravitational-wave events detected today, however, primarily occur at low ormoderate redshifts due to current interferometer sensitivity, thereforelimiting our ability to probe the high redshift behavior of these quantities.In this work, we circumvent this limitation by using an additional source ofinformation: observational limits on the gravitational-wave background fromunresolved binaries in the distant Universe. Using current gravitational-wavedata from the first three observing runs of LIGO-Virgo-KAGRA, we combinecatalogs of directly detected binaries and limits on the stochastic backgroundto constrain the time-delay distribution and metallicity dependence of binaryblack hole evolution. Looking to the future, we also explore how theseconstraints will be improved at the Advanced LIGO A+ sensitivity. We concludethat, although binary black hole formation cannot be strongly constrained withtoday's data, the future detection (or a non-detection) of thegravitational-wave background with Advanced LIGO A+ will carry strongimplications for the evolution of binary black holes.

The metallicity dependence and evolutionary times of merging binary  black holes: Combined constraints from individual gravitational-wave  detections and the stochastic background