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 due to its dependence on the metallicity of the parent
stars. In this work, 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.
This analysis sheds light on multiple new aspects of the BBH formation channel
and mass distribution. We obtain interesting constraints on the minimum delay
time between the formation of stars and mergers of BBHs $t^{\rm min}_d =
1.95^{+0.97}_{-0.93}$ Gyrs, along with a hint towards a steeper power-law form
of the delay time distribution ($(t_d)^{d}$) with an index $d < -1.55$ at
68$\%$ C.L. The mass distribution of the BBHs agrees with a power-law form with
a Gaussian peak at $\mu_g=40.26^{+1.04}_{-2.32} $ $\rm M_\odot$ which agrees
with the theoretical prediction of the lower edge of the PISN mass scale and
differs from the previous analysis. This analysis sheds light on the lower edge
of the PISN mass scale of black holes and provides hints toward the formation
channel of the BBH systems that are different from the usual fiducial scenario
with a power-law index $d=-1$. Our results are consistent with the scenarios of
varying (or fixed) Hubble constant and also for events with lower matched
filtering network signal to noise ratio.
