GWTC-4.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation

TL;DR

GWTC-4.0 enables robust cosmological and gravity tests via a hierarchical Bayesian analysis that jointly models CBC population properties and cosmology, incorporating both dark sirens (galaxy catalog–assisted) and the bright siren GW170817. The approach marginalizes over population models (PLP, MLTP, FullPop-4.0) and leverages galaxy data from GLADE+ to constrain the luminosity-distance–redshift relation, yielding $H_0 = 76.6^{+13.0}_{-9.5}$ km s$^{-1}$ Mpc$^{-1}$ (68.3% CI) when combined with the bright siren; GR-consistent constraints on modified GW propagation are reported via two parametrizations, $\Xi_0$ and $c_M$. The mass-spectrum features, especially under the FullPop-4.0 model, drive strong spectral-siren information that tightens $H_0$ constraints and informs the CBC rate evolution, while catalog completeness limits the direct gain from host information. Overall, the study demonstrates the power of GW standard sirens—especially when population and selection effects are properly marginalized— to probe the expansion history and gravity on cosmological scales, with promising improvements anticipated from deeper galaxy catalogs and more localized future GW detections.

Abstract

We analyze data from 142 of the 218 gravitational-wave (GW) sources in the fourth LIGO-Virgo-KAGRA Collaboration (LVK) Gravitational-Wave Transient Catalog (GWTC-4.0) to estimate the Hubble constant $H_0$ jointly with the population properties of merging compact binaries. We measure the luminosity distance and redshifted masses of GW sources directly; in contrast, we infer GW source redshifts statistically through i) location of features in the compact object mass spectrum and merger rate evolution, and ii) identifying potential host galaxies in the GW localization volume. Probing the relationship between source luminosity distances and redshifts obtained in this way yields constraints on cosmological parameters. We also constrain parameterized deviations from general relativity which affect GW propagation, specifically those modifying the dependence of a GW signal on the source luminosity distance. Assuming our fiducial model for the source-frame mass distribution and using GW candidates detected up to the end of the fourth observing run (O4a), together with the GLADE+ all-sky galaxy catalog, we estimate $H_0 = 76.6^{+13.0}_{-9.5} (76.6^{+25.2}_{-14.0})$ km s$^{-1}$ Mpc$^{-1}$. This value is reported as a median with 68.3% (90%) symmetric credible interval, and includes combination with the $H_0$ measurement from GW170817 and its electromagnetic counterpart. Using a parametrization of modified GW propagation in terms of the magnitude parameter $Ξ_0$, we estimate $Ξ_0 = 1.2^{+0.8}_{-0.4} (1.2^{+2.4}_{-0.5})$, where $Ξ_0 = 1$ recovers the behavior of general relativity.

Figures (13)

• Figure 1: Qualitative graphical representation of the three source-frame mass models considered in this paper and described in Section \ref{['subsubsec:population_models']} and Appendix \ref{['sec:appendix_pop']}. The mass distribution models displayed in the first two panels represent the mass ranges of BH, while the third panel includes both BH NS. The mass ranges shown are not to scale.
• Figure 2: Cumulative distribution of the size of the 90$\%$CR of the sky localization of CBC candidates observed during O1+O2+O3+O4a in orange (142 total events including GW170817) and O4a-only in blue (76 events). It can be seen that the typical sky localization of O4a events was larger than that of O1--O3 events.
• Figure 3: Top panel: Completeness fraction of GLADE+ in the K–band, indicating the probability that the catalog contains the host galaxy of a GW event, as a function of redshift for $H_0 = 67.9\ \mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$ and $\Omega_{\mathrm{m}} = 0.3065$. The different curves are calculated for a given percentage of sky coverage computed by dividing the sky in equal sized pixels of 3.35 deg$^2$, for which the apparent magnitude threshold is brighter than the corresponding $m_{\mathrm{thr}}$ value reported in the legend. The fraction of pixels with no galaxies is ${\sim}5\%$. Bottom panel: sky map showing the GLADE+ K--band apparent magnitude threshold, $m_{\rm thr}$, generated by dividing the sky into $3.35\,\text{deg}^2$ pixels. A mask is applied that removes all pixels (white region) with $m_{\rm thr}<12.5$ in order to improve the figure readability. Also shown are the 90$\%$CR sky localizations for the 10 best-localized O4a GW events included in our analysis.
• Figure 4: Hubble constant posterior for different cases. Yellow curve: posterior obtained from the bright siren GW170817 and its EM counterpart. Orange curve: posterior obtained with the spectral siren method and the FullPop-4.0 mass model. Blue curve: posterior obtained using all dark sirens with GLADE+ K-band in the luminosity-weighting case ($\epsilon=1$) and the FullPop-4.0 mass model. Black curve: posterior after combining the dark and bright siren results. The pink and green shaded areas identify the 68% CI constraints on $H_0$ inferred from CMB anisotropies Planck:2015fie and in the local Universe from SH0ES Riess:2021jrx, respectively.
• Figure 5: Left panel: Hubble constant posteriors with the dark siren method using GLADE+ K-band, assuming three different mass models in the luminosity-weighting case: PLP (magenta curve), MLTP (gold curve), and FullPop-4.0 (blue curve). See Section \ref{['subsubsec:population_models']} and Appendix \ref{['sec:appendix_pop']} for definitions of these models. Right panel: Hubble constant posteriors with the dark siren analysis in the no-weighting and luminosity-weighted schemes for host galaxies (blue dashed and solid curves, respectively). All analyses assume the FullPop-4.0 mass model. See Section \ref{['subsec:redshift_prior']} for details of the galaxy weighting scheme. In both panels the pink and green shaded areas identify the $68\%$CI constraints on $H_0$ inferred, respectively, from CMB anisotropies Planck:2015fie and in the local Universe from SH0ES Riess:2021jrx.