Next-generation gravitational-wave observatories will reach farther into the Universe than currently possible, revealing black-hole mergers from early stellar binary systems such as Population III stars, whose properties are currently poorly constrained. We develop a method to infer the properties of their progenitor populations from gravitational-wave catalogs. Using Bayesian deep learning, we train an emulator for population-synthesis predictions of black-hole merger properties across redshift as a function of the initial stellar mass function, crucially accounting for systematic uncertainty due to the finite number of training simulations. Combined with a nonparametric model for star formation history, we analyze catalogs containing both Population I/II and III sources simulated with full Bayesian parameter estimation for a detector network of Cosmic Explorer and Einstein Telescope with one year of observing time. We demonstrate our ability to separate these two populations at high redshifts where both make comparable contributions to the black-hole merger rate, excluding a Population III merger rate of zero at nearly 100% credibility. Moreover, we can place meaningful constraints on the Population III progenitor distributions; in particular, we constrain the spectral index of the initial mass function to within roughly $\pm 0.5$ of the true value and the log of the star formation rate density to within $\sim 25\%$ over redshifts 10 to 20. By leveraging astrophysics-informed and astrophysics-agnostic models, we demonstrate the discriminative power of our combined inference approach and highlight the potential of next-generation gravitational-wave observatories to uncover the details of high-redshift stellar populations.

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• Gravitational wave sources
• Binary stars