Gravitational-wave constraints on $H_0$ are robust to (putative) redshift evolution in the binary black hole mass spectrum at current sensitivity

TL;DR

This study assesses the robustness of gravitational-wave based measurements of the Hubble constant against potential redshift evolution in the binary black hole mass spectrum, finding current results are stable.

Contribution

It explicitly allows for redshift evolution in the mass spectrum model and demonstrates that current $H_0$ constraints are not significantly affected by this evolution.

Findings

No compelling evidence for mass spectrum evolution at current sensitivity.

Redshift evolution causes a modest, non-significant shift in $H_0$ towards lower values.

Systematic uncertainty from evolution is smaller than from other spectral modeling choices.

Abstract

Spectral-siren cosmology constrains the Hubble constant $H_0$ using gravitational-wave observations of compact-binary coalescences. The method combines luminosity distances inferred from the waveform with redshift information statistically encoded in population features of the source-frame mass spectrum. Because the detector measures redshifted masses, structure in the intrinsic mass distribution acts as an internal ``ruler'', making the inference sensitive to assumptions about the population model. In particular, redshift evolution of the mass spectrum is widely discussed as a potential systematic for $H_0$ measurements. We revisit spectral-siren constraints with the GWTC-4.0 binary black hole catalog, explicitly allowing the main mass scales of a standard parametric mass model to evolve with redshift. We find no compelling evidence for evolution at current sensitivity. Allowing evolution produces a modest, non--statistically--significant shift of the $H_0$ posterior toward lower values, which we interpret with targeted posterior and event-level diagnostics. Importantly, the associated systematic uncertainty is subdominant to that induced by alternative redshift-independent descriptions of the mass spectrum, such as the number of spectral features and the functional form used to model them. Our results indicate that, at current sensitivity, spectral-siren constraints on $H_0$ are robust to redshift evolution of the mass spectrum within the flexibility explored here. Using injection studies, we show that this mild $H_0$ shift is reproduced when a non-evolving underlying population is analyzed with an evolving model, consistent with an over-flexible population description at the present signal-to-noise. The sign and magnitude of the shift can, however, depend on detector sensitivity and redshift reach as the population features become increasingly constrained directly by the data.