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Scalable dark siren cosmology with gwcosmo: GPU acceleration, validation, and systematics

Alexander Papadopoulos1,*, Christian E. A. Chapman-Bird2,1, Rachel Gray1, Christopher Messenger1, and Tom Bertheas3,4

  • *Contact author: a.papadopoulos.1@research.gla.ac.uk
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Phys. Rev. D 114, 063528 – Published 15 September, 2026

DOI: https://doi.org/10.1103/53c5-mtk5

Abstract

As the number of confident gravitational-wave detections grows, population-level hierarchical analyses face increasing computational costs. Dark-siren cosmological inference integrates over the localisation volume of each gravitational-wave source. To remain feasible without discarding information from the quieter but more numerous sources in the catalog, significant efficiency improvements are vital for analysis pipelines. In this work, we present an upgraded version of the cosmological inference pipeline gwcosmo, which leverages vectorisation on graphics processing units to process the entire gravitational-wave catalog in parallel with each iteration. This new implementation achieves a speed-up of ∼103 over the previous version, facilitating analyses of O5-like numbers of GW events on wall-clock timescales of hours. Our results demonstrate the scalability of the gwcosmo pipeline, specifically its ability to handle the increasing computational load of expanding event catalogs, positioning it as a vital tool for future advances in dark-siren cosmology.

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References (63)

  1. B. F. Schutz, Determining the Hubble constant from gravitational wave observations, Nature (London) 323, 310 (1986).
  2. D. E. Holz and S. A. Hughes, Using gravitational-wave standard sirens, Astrophys. J. 629, 15 (2005).
  3. M. Moresco et al., Unveiling the universe with emerging cosmological probes, Living Rev. Relativity 25, 6 (2022).
  4. C. Messenger and J. Read, Measuring a cosmological distance-redshift relationship using only gravitational wave observations of binary neutron star coalescences, Phys. Rev. Lett. 108, 091101 (2012).
  5. S. Nissanke, D. E. Holz, S. A. Hughes, N. Dalal, and J. L. Sievers, Exploring short gamma-ray bursts as gravitational-wave standard sirens, Astrophys. J. 725, 496 (2010).
  6. B. P. Abbott et al., A gravitational-wave standard siren measurement of the Hubble constant, Nature (London) 551, 85–88 (2017).
  7. M. Mancarella, F. Iacovelli, S. Foffa, N. Muttoni, and M. Maggiore, Accurate standard siren cosmology with joint gravitational-wave and γ-ray burst observations, Phys. Rev. Lett. 133, 261001 (2024).
  8. A. Cozzumbo, U. Dupletsa, R. Calderón, R. Murgia, G. Oganesyan, and M. Branchesi, Model-independent cosmology with joint observations of gravitational waves and γ-ray bursts, J. Cosmol. Astropart. Phys. 05 (2025) 021.
  9. D. F. Chernoff and L. S. Finn, Gravitational radiation, inspiraling binaries, and cosmology, Astrophys. J. Lett. 411, L5 (1993).
  10. S. R. Taylor, J. R. Gair, and I. Mandel, Cosmology using advanced gravitational-wave detectors alone, Phys. Rev. D 85, 023535 (2012).
  11. W. M. Farr, M. Fishbach, J. Ye, and D. E. Holz, A future percent-level measurement of the Hubble expansion at redshift 0.8 with Advanced LIGO, Astrophys. J. Lett. 883, L42 (2019).
  12. J. M. Ezquiaga and D. E. Holz, Jumping the gap: Searching for LIGO’s biggest black holes, Astrophys. J. Lett. 909, L23 (2021).
  13. J. M. Ezquiaga and D. E. Holz, Spectral sirens: Cosmology from the full mass distribution of compact binaries, Phys. Rev. Lett. 129, 061102 (2022).
  14. G. Pierra and A. Papadopoulos, Heavy black-holes also matter in standard siren cosmology, arXiv:2601.03257.
  15. M. Tagliazucchi, M. Moresco, A. Agapito, M. Mancarella, S. Ferraiuolo, S. Mastrogiovanni, N. Borghi, F. Pannarale, and D. Bonacorsi, Pushing spectral siren cosmology into the third-generation era: A blinded mock data challenge, Astron. Astrophys. 711, A120 (2026).
  16. T. Bertheas, V. Gennari, D. Steer, and N. Tamanini, Spectral sirens cosmology from binary black holes populations with sharper mass features, arXiv:2603.06792.
  17. W. Del Pozzo, Inference of cosmological parameters from gravitational waves: Applications to second generation interferometers, Phys. Rev. D 86, 043011 (2012).
  18. M. Soares-Santos et al., First measurement of the Hubble constant from a dark standard siren using the dark energy survey galaxies and the LIGO/Virgo binary–black-hole merger GW170814, Astrophys. J. Lett. 876, L7 (2019).
  19. A. Palmese et al., A statistical standard siren measurement of the Hubble constant from the LIGO/Virgo gravitational wave compact object merger GW190814 and dark energy survey galaxies, Astrophys. J. Lett. 900, L33 (2020).
  20. A. Finke, S. Foffa, F. Iacovelli, M. Maggiore, and M. Mancarella, Cosmology with LIGO/Virgo dark sirens: Hubble parameter and modified gravitational wave propagation, J. Cosmol. Astropart. Phys. 08 (2021) 026.
  21. S. Mastrogiovanni, K. Leyde, C. Karathanasis, E. Chassande-Mottin, D. A. Steer, J. Gair, A. Ghosh, R. Gray, S. Mukherjee, and S. Rinaldi, On the importance of source population models for gravitational-wave cosmology, Phys. Rev. D 104, 062009 (2021).
  22. R. Gray, C. Messenger, and J. Veitch, A pixelated approach to galaxy catalogue incompleteness: Improving the dark siren measurement of the Hubble constant, Mon. Not. R. Astron. Soc. 512, 1127 (2022).
  23. S. Mastrogiovanni, D. Laghi, R. Gray, G. C. Santoro, A. Ghosh, C. Karathanasis, K. Leyde, D. A. Steer, S. Perries, and G. Pierra, Joint population and cosmological properties inference with gravitational waves standard sirens and galaxy surveys, Phys. Rev. D 108, 042002 (2023).
  24. N. Borghi, M. Mancarella, M. Moresco, M. Tagliazucchi, F. Iacovelli, A. Cimatti, and M. Maggiore, Cosmology and astrophysics with standard sirens and galaxy catalogs in view of future gravitational wave observations, Astrophys. J. 964, 191 (2024).
  25. J. Aasi et al. (LIGO Scientific Collaboration), Advanced LIGO, Classical Quantum Gravity 32, 074001 (2015).
  26. F. Acernese et al. (Virgo Collaboration), Advanced Virgo: A second-generation interferometric gravitational wave detector, Classical Quantum Gravity 32, 024001 (2015).
  27. T. Akutsu et al., Overview of KAGRA: Detector design and construction history, Prog. Theor. Exp. Phys. 2021, 05A101 (2020).
  28. B. Abbott et al., GWTC-1: A gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs, Phys. Rev. X 9, 031040 (2019).
  29. R. Abbott et al., GWTC-2: Compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run, Phys. Rev. X 11, 021053 (2021).
  30. R. Abbott et al., GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023).
  31. A. G. Abac et al., GWTC-4.0: Updating the gravitational-wave transient catalog with observations from the first part of the fourth LIGO-Virgo-KAGRA observing run, Astrophys. J. Lett. 1004, L22 (2026).
  32. R. Gray, I. M. n. Hernandez, H. Qi, A. Sur, P. R. Brady, H.-Y. Chen, W. M. Farr, M. Fishbach, J. R. Gair, A. Ghosh, D. E. Holz, S. Mastrogiovanni, C. Messenger, D. A. Steer, and J. Veitch, Cosmological inference using gravitational wave standard sirens: A Mock data analysis, Phys. Rev. D 101, 122001 (2020).
  33. R. Gray, F. Beirnaert, C. Karathanasis, B. Revenu, C. Turski, A. Chen, T. Baker, S. Vallejo, A. E. Romano, T. Ghosh, A. Ghosh, K. Leyde, S. Mastrogiovanni, and S. More, Joint cosmological and gravitational-wave population inference using dark sirens and galaxy catalogues, J. Cosmol. Astropart. Phys. 12 (2023) 023.
  34. S. Mastrogiovanni, D. Laghi, R. Gray, G. C. Santoro, A. Ghosh, C. Karathanasis, K. Leyde, D. A. Steer, S. Perries, and G. Pierra, Joint population and cosmological properties inference with gravitational waves standard sirens and galaxy surveys, Phys. Rev. D 108, 042002 (2023).
  35. S. Mastrogiovanni, G. Pierra, S. Perriès, D. Laghi, G. C. Santoro, A. Ghosh, R. Gray, C. Karathanasis, and K. Leyde, Icarogw: A Python package for inference of astrophysical population properties of noisy, heterogeneous and incomplete observations, Astron. Astrophys. 682, A167 (2024).
  36. M. Tagliazucchi, M. Moresco, N. Borghi, and M. Fiebig, Accelerating the standard siren method: Improved constraints on modified gravitational-wave propagation with future data, Astron. Astrophys. 702, A244 (2025).
  37. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Constraints on the cosmic expansion rate and modified gravitational-wave propagation, Astrophys. J. Lett. 1007, L17 (2026).
  38. I. Mandel, W. M. Farr, and J. R. Gair, Extracting distribution parameters from multiple uncertain observations with selection biases, Mon. Not. R. Astron. Soc. 486, 1086 (2019).
  39. S. Vitale, D. Gerosa, W. M. Farr, and S. R. Taylor, Inferring the properties of a population of compact binaries in presence of selection effects, in Handbook of Gravitational Wave Astronomy (Springer, Singapore, 2021), pp. 1–60.
  40. M. Fishbach, D. E. Holz, and W. M. Farr, Does the black hole merger rate evolve with redshift?, Astrophys. J. Lett. 863, L41 (2018).
  41. W. M. Farr, Accuracy requirements for empirically measured selection functions, Res. Not. AAS 3, 66 (2019).
  42. C. Talbot and J. Golomb, Growing pains: Understanding the impact of likelihood uncertainty on hierarchical Bayesian inference for gravitational-wave astronomy, Mon. Not. R. Astron. Soc. 526, 3495 (2023).
  43. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, Pytorch: An imperative style, high-performance deep learning library, arXiv:1912.01703.
  44. J. Nickolls, I. Buck, M. Garland, and K. Skadron, Scalable parallel programming with CUDA, Queueing Syst. Theory Appl. 6, 40 (2008).
  45. S. K. Lam, A. Pitrou, and S. Seibert, Numba: A LLVM-based Python JIT compiler, in Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC (New York, NY, Association for Computing Machinery, 2015), pp. 1–6.
  46. B. P. Abbott et al., Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA, Living Rev. Relativity 23, 3 (2020).
  47. G. Ashton et al., BILBY: A user-friendly Bayesian inference library for gravitational-wave astronomy, Astrophys. J. Suppl. Ser. 241, 27 (2019).
  48. M. J. Williams, Nested sampling with normalizing flows for gravitational-wave inference, Phys. Rev. D 103, 103006 (2021).
  49. M. J. Williams, J. Veitch, and C. Messenger, Importance nested sampling with normalising flows, Mach. Learn. Sci. Tech. 4, 035011 (2023).
  50. A. G. Abac et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), GWTC-4.0: Population properties of merging compact binaries, Astrophys. J. Lett. 1005, L51 (2026).
  51. S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951).
  52. D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley Series in Probability and Statistics (Wiley, New York, 2009).
  53. B. W. Silverman, Density estimation for statistics and data analysis (Chapman and Hall, London, 1986).
  54. R. Wilcox, Introduction to Robust Estimation and Hypothesis Testing, 5th ed. (Academic Press, San Diego, CA, 2021).
  55. I. McMahon, D. Laghi, M. Soares-Santos, K. Ackley, G. Dálya, Y. Gençel, D. Sánchez-Cid, F. Andrade-Oliveira, S. MacBride, C. Chapman-Bird, R. Gray, and A. Papadopoulos, Measurement of the Hubble constant using the dark energy survey year 6 gold galaxy catalog and the fourth gravitational-wave transient catalog, Mon. Not. R. Astron. Soc. 550, stag1167 (2026).
  56. R. Abbott et al. (LIGO Scientific, Virgo, and KAGRA Collaborations), Population properties of compact objects from the second LIGO–Virgo gravitational-wave transient catalog, Astrophys. J. Lett. 913, L7 (2021).
  57. P. Madau and M. Dickinson, Cosmic star-formation history, Annu. Rev. Astron. Astrophys. 52, 415 (2014).
  58. R. Essick et al., Compact binary coalescence sensitivity estimates with injection campaigns during the LIGO-Virgo-KAGRA Collaborations’ fourth observing run, Phys. Rev. D 112, 102001 (2025).
  59. I. M. Romero-Shaw et al., Bayesian inference for compact binary coalescences with Bilby: Validation and application to the first LIGO–Virgo gravitational-wave transient catalogue, Mon. Not. R. Astron. Soc. 499, 3295 (2020).
  60. G. Ashton and C. Talbot, Bilby-MCMC: An MCMC sampler for gravitational-wave inference, Mon. Not. R. Astron. Soc. 507, 2037 (2021).
  61. M. Menéndez, J. Pardo, L. Pardo, and M. Pardo, The Jensen-Shannon divergence, J. Franklin Inst. 334, 307 (1997).
  62. ODYSSEE-MURE, Odyssee database: Energy efficiency indicators and consumption trends, https://www.odyssee-mure.eu/ (2023) (accessed: 2026-05-06).
  63. N. Aghanim et al., Planck 2018 results: VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).

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Phys. Rev. D 114, 063528– Published 15 September, 2026
  • Received 5 June 2026
  • Accepted 25 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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