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 $t^{\rm min}_d =
    1.57^{+1.12}_{-0.88}$ Gyrs, along with a hint towards a steeper power-law form
    of the delay time distribution ($(t^{\rm min}_d)^{d}$) with an index
    $-d=2.54^{+0.9}_{-1.03}$ at 68$\%$ C.L. The mass distribution of the BBHs
    agrees with a power-law form with a Gaussian peak at
    $\mu_g=44.35^{+7.93}_{-6.34} $ $\rm M_\odot$ 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 $d=-1$.

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