The redshift dependence of black hole mass distribution: Is it reliable
  for standard sirens cosmology?
  An upper limit on the mass of a black hole set by the pair-instability
supernovae (PISN) process can be useful in inferring the redshift of the
gravitational wave (GW) sources by lifting the degeneracy between mass and
redshift. However, for this technique to work, it is essential that the PISN
mass-scale is redshift independent or at least has a predictable redshift
dependence. We show that the observed PISN mass-scale is likely to exhibit a
strong redshift dependence due to a non-zero value of the delay time between
the formation of a star and the merging of two black holes. This will lead to a
merger of black holes formed at a different cosmic time, over which the stellar
metallicity of the parent star can vary significantly. As a result, the
observed PISN mass scale inferred from GW sources will be redshift dependent.
Due to the unknown form of the delay-time distribution, the redshift dependence
of the PISN mass cut-off of the binary black holes (BBHs) cannot be well
characterized and will exhibit a large variation with the change in redshift.
As a result, the use of a fixed PISN mass scale to infer the redshift of the
BBHs from the observed masses will be systematically biased. Though this
uncertainty is not severe for the third observation run conducted by the
LIGO-Virgo-KAGRA collaboration, in the future this uncertainty will cause a
systematic error in the redshift inferred from PISN mass scale. The
corresponding systematic error will be a bottleneck in achieving a few percent
precision measurements of the cosmological parameters using this method in the
future. The origin of the redshift dependence of the mass distribution of BBHs
proposed in this analysis will also be useful for understanding the population
of GW sources inferred using both well-detected events and the stochastic GW
background.
