Impact of the sky-averaged redshift prior on population-level cosmological inference

Determine whether using a uniform-in-comoving-volume astrophysical redshift prior rather than a sky-averaged galaxy-catalogue-informed line-of-sight redshift prior produces a significant systematic effect in population-level cosmological posteriors.

Background

The sampled implementation evaluates gravitational-wave selection effects using a simple uniform-in-comoving-volume redshift prior, while the gridded implementation averages the line-of-sight prior over the sky. Because the redshift integral enters the hierarchical likelihood raised to the number of detected events, small differences between these choices could accumulate in analyses of large event catalogues.

The authors do not expect a significant effect for the present low-completeness GLADE+ analysis, but explicitly identify the issue as requiring detailed future investigation. The unresolved question is therefore whether this approximation remains safe for deeper catalogues and larger gravitational-wave samples.

References

Because the evaluation of the integral over redshift is taken to the power of the number of detected events (see Eq. \ref{eq:hierarchical}), minor deviations may stack up in a noticeable fashion. We do not expect this to have a significant impact here due to the relatively low completeness of the galaxy catalogue (meaning that a deviation from uniform in co-moving would only happen at very low redshifts, corresponding to a relatively small fraction of the overall volume being integrated over), but we caution that this is something that should be investigated in detail in the future.

— Expanding the scope of dark siren cosmology: Inferring the population properties of gravitational wave-hosting galaxies  (2609.04991 - Gray et al., 4 Sep 2026) in Section 4, subsection “Assessment of current results”