Probing evolution in the black hole spectrum with gravitational waves catalogs

The population of black holes observed via gravitational waves currently covers the local Universe up to a redshift $z\ensuremath{\lesssim}1$, for the most massive merging binaries, or $z\ensuremath{\lesssim}0.25$ for low-mass binary black holes (BBH). Evolution of the BBH mass spectrum over cosmic time will be a significant probe of formation channels and environments. We demonstrate a reconstruction of the BBH merger rate, allowing for general dependence on binary masses and luminosity distance or redshift and accounting for selection effects, via iterative kernel density estimation (KDE) with optimized multidimensional bandwidths. Performing such reconstructions under a range of detailed assumptions, we see no significant evidence for the evolution of BBH masses with redshift, over the range where detected events are available. At most, possible trends towards an increasing merger rate with a redshift for primary masses ${m}_{1}\ensuremath{\gtrsim}50{M}_{\ensuremath{\bigodot}}$ or towards a decreasing merger rate with a redshift for primary masses ${m}_{1}\ensuremath{\lesssim}40{M}_{\ensuremath{\bigodot}}$ may be supported. We compare these findings with previous investigations and caution against overinterpreting the current, sparse data. Significantly upgraded detectors and/or facilities, and longer observing times are required to harness any correlations of the BBH mass distribution with redshift.