Binary black holes population and cosmology in new lights: Signature of PISN mass and formation channel in GWTC-3

The mass, spin, and merger rate distribution of the binary black holes (BBHs) across cosmic redshifts provide a unique way to shed light on their formation channel. Along with the redshift dependence of the BBH merger rate, the mass distribution of BBHs can also exhibit redshift dependence due to different formation channels and dependence on the metallicity of the parent stars. We explore the redshift dependence of the BBH mass distribution jointly with the merger rate evolution from the third gravitational wave (GW) catalog GWTC-3 of the LIGO-Virgo-KAGRA collaboration. We study possible connections between peak-like features in the mass spectrum of BBHs and processes related to supernovae physics and time-delay distributions. We obtain a preference for short-time delays between star formation and BBH mergers. Using a power law form for the time delay distribution ($(t^{\rm min}_d)^{d}$) we find $d<-0.7$ credible at $90\%$ interval. The mass distribution of the BBHs {could be fitted} with a power-law form with {a redshift-dependent peak feature that can be linked to the pair instability supernovae (PISN) mass scale $M_{\rm PISN}(Z_*)$ at a stellar metallicity $Z_*$. For a fiducial value of the stellar metallicity $Z_*= 10^{-4}$, we find the $\rm M_{\rm PISN}(Z_*)=44.4^{+7.9}_{-6.3} $ $\rm M_\odot$.} This is in accordance with the theoretical prediction of the lower edge of the PISN mass scale and differs from previous analyses. Although we find a strong dependence of the PISN value on metallicity, the model that we explored is not strongly favored over those that do not account for metallicity as the Bayes factors are inconclusive. In the future with more data, evidence towards metallicity dependence of the PISN will have a significant impact on our understanding of stellar physics.