Are all Binary Black Holes Detected by LIGO-Virgo-KAGRA Following the Universal Time-Delay Distributions? Probably Not
The delay time distribution (DTD) of binary black hole (BBH) mergers encodes the evolutionary link between stellar formation history and gravitational-wave (GW) emission. We present a non-parametric reconstruction of the DTD using BBHs from the GWTC-4 catalog, employing a grid-based framework that avoids restrictive power-law assumptions. We divide the BBH population into two mass bins, $20$--$40\,M_\odot$ and $40$--$100\,M_\odot$, and reconstruct the DTD independently for each bin using grid-based trajectories, under three different star formation rate density (SFRD) models. We find that both mass bins favor an extended plateau of intermediate-to-long delay times rather than a single characteristic timescale, and that in both bins the reconstructed merger rate $\mathcal{R}(z)$ rises from its local value to a peak at intermediate redshift before declining. The two bins differ in degree rather than kind: the $20$--$40\,M_\odot$ bin is broadly constrained, with a local rate of $R_0 \approx 18$--$23\,\mathrm{Gpc^{-3}\,yr^{-1}}$ and a merger rate peaking at $z \sim 0.8$--$1.05$, while the $40$--$100\,M_\odot$ bin prefers a more sharply defined intermediate delay range of $\sim$2--4 Gyr with a steeper suppression of long delay times, within a noticeably tighter set of high-evidence trajectories, a lower local rate of $R_0 \approx 9$--$13\,\mathrm{Gpc^{-3}\,yr^{-1}}$, and a peak shifted to slightly higher redshift, $z \sim 1.0$--$1.05$. The results indicate that a single power-law DTD may not be sufficient to simultaneously describe both mass bins, pointing toward possible mass-dependent binary evolution pathways that merit further investigation with larger GW catalogs.