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Gravitational waves (GW) emitted by merging black holes (BH) and neutron stars are now routinely detected. Those are the afterlives of massive stars that formed all across the Universe—at different cosmic times and with different metallicities. Birth metallicity plays an important role in the evolution of massive stars. Consequently, the population properties of mergers are sensitive to the metallicity dependent cosmic star formation history (fSFR(Z,z)). In particular, within the isolated formation scenarios (the focus of this paper), a strong low metallicity preference of the formation of BH mergers is found. The origin of this dependence and its consequences are discussed. Most importantly, uncertainty in the fSFR(Z,z) (substantial even at low redshifts) cannot be ignored in the models. This poses a challenge for the interpretation of the observed GW source population properties. Possible improvements and the role of future GW detectors are considered. Recent efforts to determine fSFR(Z,z) and the factors that dominate its uncertainty are summarized. Many of those factors stem from the uncertain properties of faint and distant galaxies. The fact that they leave imprint on the redshift‐dependent properties of mergers makes GW a promising (and complementary to electromagnetic observations) tool to study galaxy chemical evolution. [ABSTRACT FROM AUTHOR]

Making the most of the rapidly increasing population of gravitational-wave detections of black hole (BH) and neutron star (NS) mergers requires comparing observations with population synthesis predictions. In this work, we investigate the combined impact from the key uncertainties in population synthesis modelling of the isolated binary evolution channel: the physical processes in massive binary-star evolution and the star formation history as a function of metallicity, Z , and redshift z , |$\mathcal {S}(Z,z)$|⁠. Considering these uncertainties, we create 560 different publicly available model realizations and calculate the rate and distribution characteristics of detectable BHBH, BHNS, and NSNS mergers. We find that our stellar evolution and |$\mathcal {S}(Z,z)$| variations can combined impact the predicted intrinsic and detectable merger rates by factors in the range 102–104. We find that BHBH rates are dominantly impacted by |$\mathcal {S}(Z,z)$| variations, NSNS rates by stellar evolution variations and BHNS rates by both. We then consider the combined impact from all uncertainties considered in this work on the detectable mass distribution shapes (chirp mass, individual masses, and mass ratio). We find that the BHNS mass distributions are predominantly impacted by massive binary-star evolution changes. For BHBH and NSNS, we find that both uncertainties are important. We also find that the shape of the delay time and birth metallicity distributions are typically dominated by the choice of |$\mathcal {S}(Z,z)$| for BHBH, BHNS, and NSNS. We identify several examples of robust features in the mass distributions predicted by all 560 models, such that we expect more than 95 per cent of BHBH detections to contain a BH |$\gtrsim 8\, \rm {M}_{\odot }$| and have mass ratios ≲ 4. Our work demonstrates that it is essential to consider a wide range of allowed models to study double compact object merger rates and properties. Conversely, larger observed samples could allow us to decipher currently unconstrained stages of stellar and binary evolution. [ABSTRACT FROM AUTHOR]