[Paper Review] Cosmology with LIGO/Virgo dark sirens: Hubble parameter and modified gravitational wave propagation

Andreas Finke, Stefano Foffa+3 more|arXiv (Cornell University)|Jan 29, 2021

Pulsars and Gravitational Waves Research164 references127 citations

TL;DR

This paper advances cosmological inference from LIGO/Virgo 'dark sirens'—gravitational wave events without electromagnetic counterparts—by introducing improved statistical methods for cross-correlating gravitational wave triggers with galaxy catalogs. It achieves the tightest H₀ constraint from dark sirens alone (H₀ = 67.3⁺²⁷.⁶₋₁₇.₉ km s⁻¹ Mpc⁻¹) and provides competitive limits on modified gravitational wave propagation (Ξ₀ = 2.1⁺³.²₋₁.²), demonstrating the method's robustness and potential for future cosmological constraints with increasing data volume.

ABSTRACT

We present a detailed study of the methodology for correlating `dark sirens' (compact binaries coalescences without electromagnetic counterpart) with galaxy catalogs. We propose several improvements on the current state of the art, and we apply them to the GWTC-2 catalog of LIGO/Virgo gravitational wave (GW) detections, and the GLADE galaxy catalog, performing a detailed study of several sources of systematic errors that, with the expected increase in statistics, will eventually become the dominant limitation. We provide a measurement of $H_0$ from dark sirens alone, finding as the best result $H_0=67.3^{+27.6}_{-17.9}\,\,{ m km}\, { m s}^{-1}\, { m Mpc}^{-1}$ ($68\%$ c.l.) which is, currently, the most stringent constraint obtained using only dark sirens. Combining dark sirens with the counterpart for GW170817 we find $H_0= 72.2^{+13.9}_{-7.5} \,{ m km}\, { m s}^{-1}\, { m Mpc}^{-1}$. We also study modified GW propagation, which is a smoking gun of dark energy and modifications of gravity at cosmological scales, and we show that current observations of dark sirens already start to provide interesting limits. From dark sirens alone, our best result for the parameter $\Xi_0$ that measures deviations from GR (with $\Xi_0=1$ in GR) is $\Xi_0=2.1^{+3.2}_{-1.2}$. We finally discuss limits on modified GW propagation under the tentative identification of the flare ZTF19abanrhr as the electromagnetic counterpart of the binary black hole coalescence GW190521, in which case our most stringent result is $\Xi_0=1.8^{+0.9}_{-0.6}$. We release the publicly available code $ t{DarkSirensStat}$, which is available under open source license at \url{https://github.com/CosmoStatGW/DarkSirensStat}.

Motivation & Objective

• To improve the statistical methodology for associating dark sirens with galaxy catalogs to reduce systematic errors in cosmological parameter estimation.
• To provide the tightest constraint on the Hubble constant H₀ using only dark sirens, independent of electromagnetic counterparts.
• To test for deviations from General Relativity in gravitational wave propagation using current dark siren data.
• To evaluate the impact of different catalog completeness measures and galaxy weighting schemes on cosmological inference.
• To release open-source code (DarkSirensStat) for reproducible analysis of dark siren cosmology.

Proposed method

• Develops a hierarchical Bayesian framework to compute the posterior probability of H₀ and modified gravity parameters (Ξ₀) using gravitational wave data and galaxy catalog information.
• Introduces a direction-dependent notion of catalog completeness using both mask completeness and cone completeness to better model observational selection effects.
• Proposes novel completion techniques—homogeneous and multiplicative completion—to account for missing galaxies in incomplete catalogs, improving prior accuracy.
• Applies luminosity-weighted galaxy priors (K-band and B-band) to account for galaxy distribution and detectability, with a threshold parameter Pth to control completeness.
• Computes normalization factors β(H₀) and β(Ξ₀) using Monte Carlo integration and semi-analytical approximations, incorporating realistic detection models and source parameter distributions.
• Uses the GWTC-2 catalog of LIGO/Virgo detections and the GLADE galaxy catalog to perform joint inference on H₀ and Ξ₀, with sensitivity to modified gravity.

Experimental results

Research questions

• RQ1 What is the tightest possible constraint on the Hubble constant H₀ achievable using only dark sirens from the LIGO/Virgo GWTC-2 catalog?
• RQ2 How do different methods for handling incomplete galaxy catalogs (e.g., mask vs. cone completeness, homogeneous vs. multiplicative completion) affect the inferred H₀ and Ξ₀?
• RQ3 Can current dark siren data already provide meaningful constraints on modified gravitational wave propagation, a potential signature of dark energy or modified gravity?
• RQ4 What is the impact of galaxy luminosity weighting (K-band vs. B-band) and completeness thresholds (Pth) on the robustness and precision of cosmological inference?
• RQ5 How do systematic errors from catalog incompleteness and selection effects scale with increasing event statistics, and can they be mitigated with improved modeling?

Key findings

• The study reports the tightest H₀ constraint from dark sirens alone: H₀ = 67.3⁺²⁷.⁶₋₁₇.₉ km s⁻¹ Mpc⁻¹ (68% credible interval), representing a significant improvement over prior dark siren analyses.
• When combining dark sirens with the electromagnetic counterpart of GW170817, the H₀ constraint improves to H₀ = 72.2⁺¹³.⁹₋₇.₅ km s⁻¹ Mpc⁻¹, consistent with other multi-messenger results.
• The analysis provides a competitive constraint on modified gravitational wave propagation, finding Ξ₀ = 2.1⁺³.²₋₁.² from dark sirens alone, where Ξ₀ = 1 corresponds to General Relativity.
• Under the tentative identification of ZTF19abanrhr as the electromagnetic counterpart of GW190521, the most stringent limit is Ξ₀ = 1.8⁺⁰.⁹₋₀.⁶, demonstrating sensitivity to modified gravity at cosmological scales.
• The choice of galaxy catalog completeness measure (mask vs. cone) and completion method (homogeneous vs. multiplicative) has minimal impact on the final posterior when using a high completeness threshold (Pth = 0.7), indicating robustness of the method.
• The study demonstrates that systematic errors from catalog incompleteness and selection effects will become dominant with increasing statistics, and that the proposed improvements are essential for future high-precision cosmology with dark sirens.