⚛️ general relativity

Expanding the scope of dark siren cosmology: Inferring the population properties of gravitational wave-hosting galaxies

This paper introduces an innovative methodology using a sampled redshift prior within the gwcosmo framework to jointly infer cosmological parameters and the previously unknown host galaxy weighting model from incomplete galaxy catalogues, yielding an updated Hubble constant measurement of $H_0 = 71.9^{+9.1}_{-7.5}$ km s $^{-1}$ Mpc $^{-1}$ and addressing key challenges in dark siren cosmology.

Original authors: Rachel Gray, Daniel Williams, Alexander Papadopoulos

Published 2026-09-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rachel Gray, Daniel Williams, Alexander Papadopoulos

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is expanding, and for decades, astronomers have been trying to measure exactly how fast. This rate of expansion, known as the Hubble constant, is a fundamental number that tells us the age and size of the cosmos. However, two of the most precise ways to measure it have been giving different answers. One method looks at the afterglow of the Big Bang, while another measures the light from exploding stars in nearby galaxies. The gap between these two results has grown into a major puzzle in modern physics, suggesting that either our measurements are flawed or our understanding of the universe is missing a crucial piece. To solve this, scientists have turned to a new kind of cosmic messenger: gravitational waves. These are ripples in space-time caused by violent collisions of massive objects, like black holes. Unlike light, these waves carry a built-in ruler that tells us how far away the collision happened, but they do not tell us how fast the source is moving away from us due to the expansion of the universe. To find that speed, astronomers must identify the galaxy where the collision occurred and measure its redshift, a stretching of light that reveals its velocity.

The challenge is that most of these collisions happen without any visible light, leaving astronomers with a location in the sky but no obvious host galaxy to study. This is where "dark sirens" come in. Instead of finding a single, bright host, researchers must look at a vast list of thousands of potential galaxies within the estimated location of the collision and use statistics to figure out which one is the true home. This process has been hampered by three main hurdles: the lists of galaxies are incomplete, the data on those galaxies is often simplified or compressed, and scientists have had to guess how likely a galaxy is to host a collision based on its properties. A new study by Rachel Gray and her colleagues at the University of Glasgow has introduced a flexible new method to overcome these obstacles. By treating the data on galaxies as a collection of individual samples rather than a rigid grid, they have created a system that can simultaneously figure out the expansion rate of the universe and the rules that govern which galaxies host these cosmic crashes.

The researchers applied this new approach to data from the fifth Gravitational Wave Transient Catalogue, which contains hundreds of detected collisions. They paired this data with the GLADE+ galaxy catalogue, a massive database of galaxies observed in infrared light. In the past, scientists had to make a choice: either use a simplified model that assumed all galaxies were equally likely to host a collision, or use a model that weighted galaxies by their brightness. Both choices were fixed guesses. The new method, however, allows the computer to learn the weighting rule itself. It treats the question of "which galaxy hosts the collision?" as a variable to be solved alongside the expansion rate of the universe. This means the analysis does not just assume a rule; it tests a range of possibilities and finds the one that best fits the data.

When the team ran their analysis, they found that their new method produced results consistent with previous studies that used older, less flexible techniques. This was a crucial first step, proving that the new, more complex system was working correctly. But the real breakthrough came when they let the system figure out the host galaxy rules on its own. They found that the data did not strongly favor a single, simple rule, which is expected given that the galaxy catalogue they used is not yet complete enough to provide a definitive answer. Despite this uncertainty, the method successfully combined all the available information to produce a new measurement of the Hubble constant. The result was a value of 71.9 kilometers per second per megaparsec, with a range of uncertainty that spans from roughly 64.4 to 81.0. This measurement sits between the two conflicting values that have caused the tension in the field, offering a fresh perspective that incorporates the messy reality of incomplete galaxy data.

The significance of this work lies not just in the number it produced, but in the path it opens for the future. The authors describe their work as a proof of principle, showing that it is possible to handle the complexities of real-world galaxy data without making overly simplistic assumptions. By moving away from pre-computed grids to a system that uses individual samples, they have created a tool that can adapt as our galaxy maps improve. As gravitational wave detectors become more sensitive and our lists of galaxies become more complete, this method will allow scientists to refine their measurements of the universe's expansion with unprecedented precision. It suggests that the key to solving the Hubble tension may not be a single perfect observation, but a robust statistical framework that can learn from the imperfect, incomplete data we currently have. The goal of reaching a measurement precise enough to settle the debate is now within reach, provided the tools continue to evolve alongside the data.

Technical Summary: Expanding the Scope of Dark Siren Cosmology

Problem Statement
Gravitational wave (GW) "dark siren" cosmology faces three primary challenges regarding the integration of galaxy catalogue data:

Galaxy Catalogue Incompleteness: Existing catalogues lack uniform sky coverage and are not volume-limited over the redshift ranges of detected compact binary coalescences (CBCs). Current methods typically apply pixelated incompleteness corrections with pre-computed line-of-sight (LOS) redshift priors. These pre-computed priors rely on hardcoded assumptions regarding host galaxy weighting models and incompleteness corrections, limiting flexibility.
Treatment of Redshift and Source Properties: Galaxy catalogues often provide compressed statistics (e.g., mean and standard deviation) rather than full posterior distributions for redshift and source properties (e.g., luminosity, stellar mass). This compression loses correlations between parameters, and current incompleteness correction methods have not successfully utilized full posteriors while compensating for catalogue incompleteness.
Unknown Host Galaxy Weighting Model: The relationship between host galaxy properties (e.g., stellar mass, star formation rate) and CBC formation rates is poorly defined. Previous analyses have fixed the host weighting model (e.g., luminosity-weighted) for each run, preventing the marginalization over this uncertainty.

Methodology
The authors present an updated hierarchical Bayesian framework implemented within the gwcosmo software. The core innovation is the replacement of pre-computed, gridded LOS redshift priors with a sampled redshift prior.

Sampled LOS Prior: Instead of a grid, the prior is represented by a set of samples drawn from the galaxy catalogue and an astrophysical prior for the "missing" galaxies. This allows for the joint inference of cosmological parameters ( $\Lambda_{cosmo}$ ), GW population parameters ( $\Lambda_{pop}$ ), and host galaxy population parameters ( $\Lambda_{gal}$ ).
Multi-Resolution Pixelation (OIM): To manage computational memory scaling with the number of galaxies, the authors introduce an Observationally-Informed Map (OIM). This map uses a multi-resolution scheme where "GOOD" pixels (containing well-localized GWs and galaxy catalogue coverage) use high-resolution sampling, while "BAD" pixels (poorly localized or no catalogue coverage) use a coarser, astrophysical-only prior.
Incompleteness Correction: The method marginalizes over the probability of a galaxy being in the catalogue ( $G$ ) or not ( $\bar{G}$ ). For galaxies not in the catalogue, samples are drawn from an astrophysical prior (e.g., a Schechter function) and weighted by the selection function (e.g., apparent magnitude threshold).
Dynamic Reweighting: Because the prior is sample-based, the host galaxy weighting model (parameterized by $\epsilon$ , where weights $\propto L^\epsilon$ ) can be applied on the fly during inference. This enables the marginalization over $\epsilon$ rather than fixing it a priori.

Key Contributions

Joint Inference Framework: The paper demonstrates the first methodology capable of simultaneously inferring cosmological parameters, GW population properties, and the host galaxy weighting model while accounting for galaxy catalogue incompleteness.
Sample-Based Prior Implementation: The authors successfully implemented the sampled LOS prior in gwcosmo, replacing the gridded approach. This allows for the utilization of full galaxy posteriors (where available) and flexible handling of selection effects without hardcoded assumptions.
Validation: The method was validated by reproducing a subset of GWTC-5.0 cosmology results using the GLADE+ K-band galaxy catalogue, showing statistical agreement with previous results derived using the gridded LOS prior.

Results

Consistency: Analyses of the GWTC-5.0 dataset (235 dark sirens) using the new sampled prior yielded results consistent with the previous gridded approach for both uniform ( $\epsilon=0$ ) and luminosity-weighted ( $\epsilon=1$ ) host galaxy models.
Joint Inference of Weighting Model: The authors performed a novel analysis jointly inferring the Hubble constant ( $H_0$ ) and the host galaxy weighting parameter $\epsilon$ (assuming a uniform prior in $[0, 2]$ ).
Hubble Constant Measurement: Combining the marginal posterior on $H_0$ from the dark sirens with the bright siren GW170817, the authors report an updated measurement:
$H_0 = 71.9^{+9.1}_{-7.5} \text{ km s}^{-1} \text{ Mpc}^{-1}$
(median and 68% symmetric credible interval).
Constraints on $\epsilon$ : The parameter $\epsilon$ was found to be poorly constrained by the current dataset (GLADE+ K-band), which has low completeness at the redshifts of most GWTC-5.0 detections. However, the analysis confirmed that higher values of $\epsilon$ correlate with increased structure in the LOS prior, leading to tighter $H_0$ constraints, though caution is advised against pushing $\epsilon$ to high values with current data due to potential artificial narrowing of posteriors.

Significance and Claims
The paper positions this work as a "proof of principle" that opens the door to solving the three major challenges facing dark siren cosmology from the electromagnetic side. By switching to a sampled prior, the method gains the flexibility to:

Move beyond single magnitude thresholds to handle complex selection effects (e.g., multi-band dependencies).
Utilize full galaxy posteriors, preserving correlations between redshift and source properties.
Marginalize over the unknown host galaxy weighting model, effectively inferring the population of CBC-hosting galaxies alongside cosmology.

The authors modestly note that while the method is promising, its robustness depends on having sufficient samples to represent the prior accurately, and significant developmental work is required to ensure stability as model complexity increases. They conclude that with a clear path forward and future improvements in galaxy catalogues and GW localization, the goal of a 2% measurement of $H_0$ by the mid-2030s remains attainable.

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