Cosmic Correlations: How Spins, Masses, and Redshifts Shape the Gravitational-Wave Universe

Recent gravitational-wave observations have tightly constrained the mass–redshift distribution of compact binaries, yet the role of spin within this framework remains uncertain. In particular, it is unclear whether the apparent evolution in spin magnitudes arises primarily from correlations with mass, redshift, or both. In this work, we employ various population models to disentangle these dependencies using O4 gravitational-wave data. Building on the “transition mass” model, we introduce an analogous “transition redshift” to test whether spin evolution is more strongly governed by source mass or cosmic epoch. This approach allows us to determine whether high-mass, low-redshift systems exhibit systematically different spin properties than their low-mass counterparts. We further explore alternative parameterizations, including smooth redshift-dependent spin evolution within mass bins, to assess model robustness. By connecting these population-level trends to astrophysical formation channels and cosmic star-formation histories, our results provide a window into how black hole spins have evolved over cosmic time—and offer predictive insights into the future landscape of gravitational-wave populations.