Measurement of the Hubble constant using the Dark Energy Survey Year 6 Gold galaxy catalogue and the fourth Gravitational-Wave Transient Catalogue

Technical Summary: Measurement of the Hubble Constant using DES Y6 Gold and GWTC-4.0

Problem Statement
The Hubble constant ($H_0$) tension between early-Universe (CMB) and late-Universe (supernovae) measurements remains a critical challenge in cosmology. Gravitational wave (GW) standard sirens offer an independent pathway to measure $H_0$. While "bright sirens" (events with electromagnetic counterparts, e.g., GW170817) provide direct redshift measurements, they are rare. "Dark sirens" (events without counterparts) rely on statistically correlating GW localization volumes with galaxy catalogues to infer redshift. Previous analyses using the Dark Energy Survey (DES) were limited to single events or fixed population models, and existing catalogues like GLADE+ suffer from incompleteness at $z > 0.05$. This study addresses the need to adapt deep, wide-field photometric catalogues for joint inference of cosmological and GW population parameters using the full fourth Gravitational-Wave Transient Catalogue (GWTC-4.0).

Methodology
The authors utilize the gwcosmo pipeline to perform a joint Bayesian inference of cosmological parameters ($H_0$) and compact binary coalescence (CBC) population parameters.

• Data Sources:
  • GW Events: 142 CBC candidates from GWTC-4.0 (O4a run), including 137 binary black holes and 5 candidates with potential neutron star components. GW170817 is treated separately as a bright siren.
  • Galaxy Catalogue: The DES Year 6 (Y6) Gold photometric catalogue, covering 4923 deg$^2$ with $r$-band depth of 23.9 mag.
• Catalogue Preparation and Selection:
  • Object Selection: Applied quality cuts (FLAGS_FOOTPRINT, FLAGS_FOREGROUND, FLAGS_GOLD) and star-galaxy separation using XGB_PRED (gradient boosted decision trees) to remove misclassified bright stars.
  • Redshift Range: Restricted to $0.05 < z < 0.50$. The lower cut ($z > 0.05$) mitigates CCD saturation effects in DES; the upper cut ($z < 0.5$) ensures the validity of $K$-corrections derived from SDSS filters and avoids photometric redshift biases in the $0.15 < z < 0.35$ range where $u$-band data is missing.
  • Luminosity Function: Measured the $r$-band Schechter luminosity function using the $1/V_{max}$ method to quantify catalogue completeness. Evolution parameters ($M^*(z)$, $\alpha(z)$, $\phi^*(z)$) were modeled linearly with redshift.
  • Weighting: Host galaxy probabilities were weighted by luminosity ($\epsilon=1$), assuming merger rates scale with stellar mass.
• Line-of-Sight (LOS) Redshift Prior:
  • Constructed a LOS prior combining in-catalogue galaxies (weighted by luminosity and photo-$z$ uncertainty) and an "empty catalogue" term (uniform in comoving volume) for undetected galaxies.
  • Validated the prior against the uniform assumption, noting deviations up to ~21% due to real large-scale structures (e.g., galaxy walls) and photo-$z$ biases.
• Computational Framework:
  • Implemented hardware acceleration using GPU vectorization (via PyTorch and Numba/CUDA) to handle kernel density estimates (KDEs) over posterior samples. This reduced analysis wall-time from weeks to hours, enabling the processing of hundreds of events.

Key Contributions

1. Adaptation of DES Y6 Gold: Successfully adapted the deep DES Y6 Gold catalogue for dark siren cosmology, demonstrating its utility despite covering only ~12% of the sky. The catalogue offers a galaxy density $\sim 100-1000$ times greater than GLADE+ within the footprint.
2. Joint Inference: Performed the first joint inference of $H_0$ and CBC population parameters using the full GWTC-4.0 dataset and a deep photometric catalogue, moving beyond fixed population models used in earlier DES analyses.
3. Bias Mitigation: Identified and mitigated specific biases in the DES redshift distribution, including saturation at low $z$ and photo-$z$ scattering at intermediate $z$, by applying rigorous redshift cuts ($0.05 < z < 0.5$).
4. Computational Efficiency: Demonstrated a 1–2 order of magnitude speed-up in gwcosmo via GPU acceleration, making large-scale dark siren analyses feasible for future GW catalogues.

Results

• Dark Sirens Only: Using the DES Y6 Gold catalogue with the $0.05 < z < 0.5$ cut, the study measures $H_0 = 71.7^{+22.7}_{-18.3}$ km s$^{-1}$ Mpc$^{-1}$. This represents an ~11% reduction in the 68.3% confidence interval width compared to previous O4a analyses using GLADE+.
• Combined (Dark + Bright): Combining the dark siren result with the bright siren GW170817 yields $H_0 = 73.1^{+11.9}_{-8.5}$ km s$^{-1}$ Mpc$^{-1}$. This is a ~10% improvement in precision over the O4a standard siren result.
• Constraining Power: The authors note that the majority of the constraining power on $H_0$ in this dataset comes from the "spectral siren" aspect (features in the mass distribution) rather than the galaxy catalogue itself. The galaxy catalogues currently provide a small improvement over the "empty catalogue" case because they are too narrow or shallow to cover the localization volumes of most GW events.

Significance and Claims
The paper claims to demonstrate the successful adaptation of deep galaxy surveys for GW cosmology, highlighting the methodologies required to handle catalogue incompleteness and redshift biases. The authors assert that while current constraints are limited by the depth and sky coverage of existing catalogues relative to GW localization volumes, the demonstrated framework is essential for maximizing the potential of next-generation surveys (e.g., LSST, Euclid, DESI). The work serves as a preparatory step for the era of precision GW cosmology, where future observing runs (O4b, O5) and deeper catalogues will allow dark sirens to become a primary tool for resolving the $H_0$ tension. The study emphasizes that the bulk of the improvement in precision comes from the joint inference of population parameters, with galaxy catalogues providing incremental but necessary refinements.