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 can get smeared and the position of the PISN mass-scale is likely to exhibit a strong redshift dependence due to a combined effect from the non-zero value of the delay time between the formation of a star and the merging of two black holes and the metallicity dependence of PISN mass scale. 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 the 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.