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REVIEW 4 major objections 5 minor 91 references

Ten well-localized dark sirens from one observing year can measure H0 to about one percent with a shallow galaxy catalog and one night of spectroscopy.

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2026-08-01 18:28 UTC pith:23LXISOC

load-bearing objection Promising dark siren strategy, but the 'best N in a year' bootstrap likely overstates precision — worth a referee round with a required fix. the 4 major comments →

arxiv 2607.17284 v1 pith:23LXISOC submitted 2026-07-19 astro-ph.CO gr-qc

One Year and One Night to 1% in H₀: Efficient Spectroscopic Strategy for Dark Siren Cosmology

Yixuan Dang , Ariel J. Amsellem , Ignacio Maga\~na Hernandez , Antonella Palmese , B. S. Sathyaprakash This is my paper
classification astro-ph.CO gr-qc
keywords dark sirensHubble constantgravitational-wave cosmologyvolume-limited galaxy catalogspectroscopic follow-upA# sensitivitygolden dark sirensBayesian inference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper asks how deep a galaxy catalog must be for dark siren cosmology and how much telescope time the campaign costs. Using simulated binary black hole mergers and a mock galaxy catalog, the authors claim that a volume-limited catalog reaching apparent magnitude r~19 is enough: going deeper to r~24 barely changes the answer. Combining the ten best-localized events from a single year of the A# three-detector network gives a median H0 precision of 0.98% with no bias, and the required spectroscopic follow-up fits in one night, or five under conservative assumptions. The result matters because a ~1% H0 measurement from gravitational waves would offer an independent check on the Hubble tension without waiting for third-generation detectors.

Core claim

On the paper's own terms, the central discovery is that catalog depth is not the bottleneck for well-localized dark sirens. For a sample of ten or more events, the width of the joint H0 posterior converges once the volume-limited catalog reaches r~19; a much deeper r~24 catalog changes the median fractional width by only a few percent. With the ten best-localized events in one year at A# sensitivity, the posterior is consistent with the injected H0 (offset -0.03%) and has median fractional width 0.98%, with the 84th percentile at 1.54%—still below the 2% target. The same ten-event strategy for the A+ network yields 2.63%. The authors also estimate that existing multi-object spectrographs can

What carries the argument

The dark siren (galaxy catalog) method: a joint Bayesian likelihood over gravitational-wave events in which each galaxy in the catalog contributes a delta-function prior at its sky position and redshift, with a detector-selection normalization beta(H0). The paper's specific contribution is the systematic scan of the apparent-magnitude limit r of the volume-limited sample, identifying r~19 as the point of convergence in both precision and unbiasedness for ten-event samples.

Load-bearing premise

The forecast assumes complete, unbiased spectroscopic coverage to r~19 for every one of the ten best-localized events within the year; the paper itself notes that about 20% of such events fall in the zone of avoidance, so discarding them would extend the collection period by a comparable factor.

What would settle it

Measure the actual Hubble constant from a set of well-localized dark sirens using a complete r<19 volume-limited catalog: if the recovered H0 is biased by more than the reported ~1% (or if the true host of any event is fainter than r=19 while the posterior was overconfident), the shallow-catalog strategy is refuted. A targeted version: take one golden event with a uniquely identified host at r>19 and show the r<19 posterior excludes the true H0.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A ~1% H0 measurement from dark sirens is feasible with the A# network and a modest spectroscopic program, offering an independent test of the Hubble tension.
  • A volume-limited catalog to r~19 is sufficient for well-localized events; deeper surveys add negligible precision but substantially increase follow-up cost.
  • The campaign is schedulable within a standard observing allocation: about one night optimally, five nights conservatively, with existing multi-object spectrographs.
  • With the A+ network the same ten-event strategy gives 2.63%, still a strong constraint but only 32% of realizations reach the 2% goal.
  • The unbiasedness holds even without stellar-mass weighting of hosts, though the precision degrades slightly (to about 1.36%).

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The roughly 20% of well-localized events lying in the zone of avoidance suggests the 'one year' headline implicitly assumes all-sky coverage; a realistic campaign may need about 1.25 years or a partial-sky analysis with a corresponding selection correction.
  • If photometric redshifts can be made complete to r~19 in the localization volumes, part of the spectroscopic cost could be replaced by existing imaging surveys—a testable extension the paper does not pursue.
  • The convergence at r~19 is established for simulated black-hole populations; it would be worth re-checking with a real r<19 catalog using actual events, since the simulation's luminosity–mass relation may not capture the faint end of the host distribution.
  • Combining this strategy with spectral siren population features could push the combined constraint below 1% and break degeneracies the galaxy-catalog method alone leaves.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper presents a simulation-based forecast for dark-siren measurements of the Hubble constant using the galaxy-catalog (statistical) method. The authors build a lightcone from the Uchuu-ν2GC simulation, inject a population of BBH mergers drawn from a Madau-Dickinson-like rate with stellar-mass weighting, and use GWBENCH and bilby to estimate sky localization and distance posteriors for the best-localized events in ten years of A# (HLI) and A+ (HLV) observations. They then select the best 3, 5, 10, 15 events per year via bootstrap resampling from the pooled 10×N best events, and evaluate the joint H0 posterior for volume-limited galaxy catalogs of varying depth r. The central claims are: (i) a shallow volume-limited catalog at r≈19 does not underestimate the H0 uncertainty for well-localized events relative to r≈24; (ii) combining the ten best-localized events in one year gives an unbiased H0 measurement with median precision 0.98+0.56/-0.32% for A# and 2.63+1.87/-1.53% for A+; and (iii) the required spectroscopic follow-up costs 1–5 nights on existing instruments. The paper provides detailed instrument time estimates and discusses several caveats, including the Zone of Avoidance and an unexplained small offset in the recovered median.

Significance. If the 0.98% precision and unbiasedness hold, this is an important result: it suggests that dark sirens can reach percent-level H0 constraints within a single observing year of a next-generation network, using only a modest spectroscopic campaign to r≈19. The paper's strengths include the use of a full Bayesian inference pipeline with bilby on top of a realistic injected population, the systematic exploration of catalog-depth effects, the comparison of two detector networks, and the concrete, instrument-by-instrument telescope-time estimates. The result is clearly relevant to the Hubble tension. However, the headline precision and the practical feasibility claims rest on a resampling procedure that does not reproduce per-year selection statistics and on an idealized assumption of complete spectroscopic coverage; until those are tested with a correct simulation, the central claim remains unverified.

major comments (4)
  1. [Uchuu and GW Injections, final paragraph; Figures 1–3] The 1000 realizations of 'the best N events per year' are generated by bootstrapping (sampling with replacement) from the 10×N best localized events in the ten-year dataset. This conflates a per-year order statistic with a random draw from the global best. In a real year, the number of detections is Poisson, and the top N events are the N smallest ΔΩ90 within that year's realization; poor years contribute few or no top-N events. The pooled 10×N best events preferentially exclude poor years and poor events, so this bootstrap underestimates the year-to-year variance. It also allows the same event to appear multiple times in a single realization, which is unphysical and artificially sharpens the posterior. The headline numbers (0.98+0.56/-0.32% and the 84th percentile 1.54%) and the 94% fraction in Figure 3 are all derived from this procedure. The authors should replace this with a proper s
  2. [Statistical Framework, Eq. (4); Discussion] The selection function in Eq. (4) uses a fixed ΔΩ90 threshold equal to the maximum of the best 10×N events, whereas the actual selection is a per-year order statistic. Conditioning the per-event selection probability on the pooled 10-year maximum rather than on the year-specific threshold is a misspecification; if the threshold is too loose for some realizations (or too tight for others), β(H0) will be wrong and the H0 posterior can be biased. The paper acknowledges an 'unexplained small offset' in the recovered median (Discussion) and attributes it tentatively to luminosity-distance overestimation, but the selection-function approximation is a more direct candidate. The authors should either compute β under the actual per-year selection rule or demonstrate numerically that the offset is not caused by this approximation.
  3. [Discussion, final paragraph; Abstract and claim (ii)] The paper states that roughly 20% of the well-localized events fall in the zone of avoidance, and that discarding them would extend the one-year observing period by a comparable factor. This directly qualifies the abstract and claim (ii), which present a 'single year' campaign. If ~20% of best-localized events are unusable, then collecting ten usable events requires observing for ~12–15 months (or a larger initial sample), and the forecast precision for a strictly one-year campaign should be recomputed with the selection function and event count reduced accordingly. The current text acknowledges this but does not fold it into the headline; please revise the claim or the abstract to state the effective time requirement.
  4. [Uchuu and GW Injections; Optimal Galaxy Catalog Depth] The catalog used in the analysis is a simulated, all-sky uniform catalog (five galaxies per HEALPix pixel), and the analysis assumes that complete spectroscopic coverage to r≈19 is achievable in the localization regions. In reality, survey completeness is limited by footprints, extinction, fiber collisions, and redshift failures, and the paper's instrument-time estimates assume target densities that may not be achievable in crowded fields. The claim (iii) of 'one to five nights' therefore depends on an idealized completeness model. Please quantify the impact of realistic incompleteness — e.g., by degrading the catalog with footprint/completeness maps or by adding a completeness parameter — on both the precision and the unbiasedness of the H0 posterior.
minor comments (5)
  1. [Abstract/Introduction] The network names A# and A+ are used before their sensitivity curves are defined. Please define them at first use (e.g., cite LIGO-T2300041 and LIGO-T1800044).
  2. [Figure 3 caption and text] The caption labels the vertical axis as σH0/Hmed0, while the text says 'forecast precision σH0/Hinj0 falls below the 2% target.' Clarify which denominator is used and make the caption consistent with the text.
  3. [Statistical Framework, Eq. (2)] The superscript (i) placement on β is inconsistent: β(H0|CAT(i)(H0)) appears in the denominator but the definition in Eq. (3) is written for a single event. Please make the notation uniform.
  4. [Statistical Framework, Eq. (4)] The golden/silver thresholds (ΔΩ90 < 0.1 deg2 and < 1 deg2) are defined but not used in the subsequent analysis, which simply selects the best N by ΔΩ90. State whether these thresholds are needed or remove them to avoid confusion.
  5. [End Matter, Table I] The 'All' row sums exposure+overhead for each instrument, but the main text's '1 night' / '5 nights' figures do not specify which instrument combination is being summed or the assumed usable hours per night (the text says 5–8 hours). Please clarify.

Circularity Check

0 steps flagged

No significant circularity: the H0 precision forecast is computed from simulated Bayesian inference with a fixed injected H0, not reduced to an input by construction.

full rationale

The paper's central claims are forecast results from injected simulated events. Equations (1)-(4) implement the standard dark-siren likelihood with a uniform H0 prior and a selection-function normalization; no parameter is fitted to a subset of data and then reported as a prediction of a closely related quantity. The recovered H0 distribution is generated from posterior samples with a fixed injected H0 = 67.74 km/s/Mpc, so the reported 0.98% width is a genuine inference product rather than a definitional restatement of an input. The bootstrap construction of 'one-year' realizations by resampling the 10-year best events is a statistical approximation that may understate inter-year variance, and the ΔΩ_threshold calibrated to the pooled 10N best events may misspecify the selection; but these are correctness/robustness concerns, not circular reductions: the per-realization posterior widths are still computed from the event likelihoods and galaxy catalog, not from the bootstrap itself. Self-citations (Refs. [18], [27], and the in-prep [11] lightcone paper) provide background nomenclature and data description; the present claims are demonstrated with the authors' own injections and inference, so the self-citations are not load-bearing. The paper's stated caveats (zone-of-avoidance loss, unexplained median offset) weaken realism but are disclosed limitations rather than circular steps. No step in the derivation chain equates the output to an input by definition.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

No new physical entities are introduced. The paper's central forecast rests on several adopted numerical inputs and domain assumptions: the Uchuu galaxy realization, the GWTC-4 population model, complete spectroscopic coverage, and the ad hoc selection-function threshold. These are load-bearing because they set the distribution of well-localized events and the catalog content in the inference.

free parameters (3)
  • BBH merger rate parameters (z_p, gamma, kappa, phi0) = 1.75, 2.0, 4.6, 16.16 Gpc^-3 yr^-1
    Adopted from the GWTC-4 population fit; sets the redshift distribution of injected events, which controls how many well-localized low-redshift events occur in one year.
  • Stellar-mass weighting at injection = Linear w=(M-M_min)/(M_max-M_min)
    Chosen to suppress dwarf galaxies as hosts; the authors show removing it widens the uncertainty to 1.36%, so it affects but does not drive the quoted 0.98%.
  • Selection threshold for dark-siren selection function = max ΔΩ90 of the best 10×N events in 10 years
    Ad hoc rule in Eq. (3)-(4) to compute selection bias; not justified as a model of one-year best-N selection and could bias posterior widths.
axioms (6)
  • domain assumption Flat ΛCDM with Ω_m=0.3 and luminosity distance d_L(z,H0) used throughout
    Invoked in Eq. (2); H0 inference assumes this cosmology and fixed matter density.
  • domain assumption Uchuu-v2GC simulation and its semi-analytic galaxy population represent real galaxies at z<0.5
    All host galaxies and catalog galaxies are drawn from Uchuu; there is no validation against a real complete survey.
  • domain assumption A complete spectroscopic catalog to r≈19 can be built for each localization region
    Central to claims (i) and (ii); the paper itself notes about 20% of well-localized events fall in the zone of avoidance.
  • domain assumption Detection probability P_det is accurately given by GWBENCH Fisher matrices and the threshold rule
    Eq. (4) computes beta using P(SNR>11, ΔΩ90<threshold | Ω,d_L); Fisher approximation may be inaccurate for low-SNR events.
  • domain assumption BBH population model (Broken Power Law + 2 Peaks, Gaussian Spin) from GWTC-4
    Controls injected mass, spin, and redshift distributions; adopted entirely from Ref [3] without re-validation.
  • ad hoc to paper The unexplained offset in recovered H0 is not a systematic bias
    The authors say the offset is consistent with zero but its origin remains unclear; the unbiasedness claim assumes it is statistical rather than systematic.

pith-pipeline@v1.3.0-alltime-deepseek · 17141 in / 15728 out tokens · 162941 ms · 2026-08-01T18:28:09.407407+00:00 · methodology

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read the original abstract

Gravitational-wave events from compact binary coalescences (CBCs) can be used as standard sirens: they encode the luminosity distance to their sources, which yields a measurement of the Hubble constant ($H_0$) if the source's redshift is known. In the absence of an electromagnetic counterpart, $H_0$ can still be inferred statistically from the cataloged galaxies within the event's sky localization volume via the dark siren, or galaxy catalog method. In this work we examine how the depth of a volume-limited galaxy catalog affects this inference and identify the most efficient spectroscopic strategy for an unbiased measurement of $H_0$ at a median precision of $0.98\%$. The strategy is to carry out spectroscopic surveys to a depth of $r \sim 19$ for the ten best-localized events observed in one year by the LIGO Hanford, LIGO Livingston, and LIGO-India network at A$^\#$ sensitivity. Such a campaign requires a minimum of one night of electromagnetic follow-up observations, or five nights under the most conservative assumptions. For the Hanford, Livingston, and Virgo network at A$+$ sensitivity, the same ten-event strategy yields a median precision of $2.63\%$.

Figures

Figures reproduced from arXiv: 2607.17284 by Antonella Palmese, Ariel J. Amsellem, B. S. Sathyaprakash, Ignacio Maga\~na Hernandez, Yixuan Dang.

Figure 1
Figure 1. Figure 1: FIG. 1. Fractional width [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Fractional statistical fluctuation of the joint [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Forecast [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Sky location distribution map of silver ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Median target density, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

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Reference graph

Works this paper leans on

91 extracted references · 4 canonical work pages

  1. [1]

    2026, GWTC-5.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation,https: //arxiv.org/abs/2605.27227

    Pith/arXiv arXiv 2026

  2. [2]

    2025, 4MOST Facility Capabilities,, https://www.4most.eu/cms/facility/capabilities/

    4MOST Consortium. 2025, 4MOST Facility Capabilities,, https://www.4most.eu/cms/facility/capabilities/

    2025

  3. [3]

    G., et al

    Abac, A. G., et al. 2025, GWTC-4.0: Population Proper- ties of Merging Compact Binaries,https://arxiv.org/abs/ 2508.18083

    Pith/arXiv arXiv 2025

  4. [4]

    2022, Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument, Astron

    Abareshi, B., et al. 2022, Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument, Astron. J., 164, 207, doi:10.3847/1538-3881/ac882b

    doi:10.3847/1538-3881/ac882b 2022

  5. [5]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017, A gravitational-wave standard siren measurement of the Hub- ble constant, Nature (London), 551, 85, doi:10.1038/ nature24471

    2017

  6. [6]

    2005, The Dark Energy Survey,https:// arxiv.org/abs/astro-ph/0510346

    Abbott, T., et al. 2005, The Dark Energy Survey,https:// arxiv.org/abs/astro-ph/0510346

    Pith/arXiv arXiv 2005

  7. [7]

    2016, The Dark Energy Survey: more than dark energy – an overview, Mon

    Abbott, T., et al. 2016, The Dark Energy Survey: more than dark energy – an overview, Mon. Not. Roy. Astron. Soc., 460, 1270, doi:10.1093/mnras/stw641

    doi:10.1093/mnras/stw641 2016

  8. [8]

    2024, Prospect of precision cos- mology and testing general relativity using binary black holes – galaxies cross-correlation, Mon

    Afroz, S., & Mukherjee, S. 2024, Prospect of precision cos- mology and testing general relativity using binary black holes – galaxies cross-correlation, Mon. Not. Roy. Astron. Soc., 534, 1283, doi:10.1093/mnras/stae2139

    doi:10.1093/mnras/stae2139 2024

  9. [9]

    2016, The DESI Experiment Part I: Science,Targeting, and Survey Design,https://arxiv.org/ abs/1611.00036

    Aghamousa, A., et al. 2016, The DESI Experiment Part I: Science,Targeting, and Survey Design,https://arxiv.org/ abs/1611.00036

    Pith/arXiv arXiv 2016

  10. [10]

    2020, Planck 2018 results

    Aghanim, N., et al. 2020, Planck 2018 results. VI. Cosmolog- ical parameters, Astron. Astrophys., 641, A6, doi:10.1051/ 0004-6361/201833910

    2020

  11. [11]

    J., et al

    Amsellem, A. J., et al. in prep

  12. [12]

    2019, BILBY: A user-friendly Bayesian in- ference library for gravitational-wave astronomy, Astrophys

    Ashton, G., et al. 2019, BILBY: A user-friendly Bayesian in- ference library for gravitational-wave astronomy, Astrophys. J. Suppl., 241, 27, doi:10.3847/1538-4365/ab06fc

    doi:10.3847/1538-4365/ab06fc 2019

  13. [13]

    2023, A Dark Siren Measurement of the Hub- ble Constant with the LIGO/Virgo Gravitational Wave Event GW190412 and DESI Galaxies, Res

    Ballard, W., et al. 2023, A Dark Siren Measurement of the Hub- ble Constant with the LIGO/Virgo Gravitational Wave Event GW190412 and DESI Galaxies, Res. Notes AAS, 7, 250, doi:10.3847/2515-5172/ad0eda

    doi:10.3847/2515-5172/ad0eda 2023

  14. [14]

    2018, Updated Advanced LIGO sensitivity design curve, Technical Notes, LIGO-T1800044,,https://dcc

    Barsotti, L., Fritschel, P., Evans, M., & Gras, S. 2018, Updated Advanced LIGO sensitivity design curve, Technical Notes, LIGO-T1800044,,https://dcc. ligo.org/LIGO-T1800044/public https://dcc.ligo. org/LIGO-T1800044/public

    2018

  15. [15]

    2020, Incompleteness Matters Not: Inference of𝐻 0 from Binary Black Hole–Galaxy Cross-correlations, Astrophys

    Bera, S., Rana, D., More, S., & Bose, S. 2020, Incompleteness Matters Not: Inference of𝐻 0 from Binary Black Hole–Galaxy Cross-correlations, Astrophys. J., 902, 79, doi:10.3847/ 1538-4357/abb4e0

    2020

  16. [16]

    A., & Di Mille, F

    Blanc, G. A., & Di Mille, F. 2016, Las Cam- panas Observatory Exposure Time Calculator,,https: //www.lco.cl/lcoastronomers/˜iss/lcoetc/html/ lcoetc_sspec.html

    2016

  17. [17]

    2021, GWBENCH: a novel Fisher information package for gravitational-wave benchmarking, Classical and Quantum Gravity, 38, 175014, doi:10.1088/1361-6382/ ac1618

    Borhanian, S. 2021, GWBENCH: a novel Fisher information package for gravitational-wave benchmarking, Classical and Quantum Gravity, 38, 175014, doi:10.1088/1361-6382/ ac1618

    doi:10.1088/1361-6382/ 2021

  18. [18]

    A further open question concerns the luminosity thresh- arXiv:2607.17284v1 [astro-ph.CO] 19 Jul 2026 2 old imposed on the galaxy catalog used for host identifica- tion

    and [47] identified these asgolden dark sirens, and [27] demonstrated that a combined sample of golden (localized to within 0.1 deg2) and silver (localized to within 1 deg 2) dark sirens observed over a single year can yield a few-percent constraint on𝐻 0, provided that a deep, complete spectro- scopic catalog is available within the localization volume, ...

    Pith/arXiv arXiv 2026

  19. [19]

    G., & Sathyaprakash, B

    Borhanian, S., Dhani, A., Gupta, A., Arun, K. G., & Sathyaprakash, B. S. 2020, Dark Sirens to Resolve the Hub- ble–Lemaˆıtre Tension, Astrophys. J. Lett., 905, L28, doi:10. 3847/2041-8213/abcaf5

    2020

  20. [20]

    2003, Stellar population synthesis at the resolution of 2003, Mon

    Bruzual, G., & Charlot, S. 2003, Stellar population synthesis at the resolution of 2003, Mon. Not. R. Astron. Soc., 344, 1000, doi:10.1046/j.1365-8711.2003.06897.x

    arXiv 2003

  21. [21]

    2021, Cosmology with Love: Measuring the Hubble constant using neutron star universal relations, Phys

    Chatterjee, D., Hegade K R, A., Holder, G., et al. 2021, Cosmology with Love: Measuring the Hubble constant using neutron star universal relations, Phys. Rev. D, 104, 083528, doi:10.1103/PhysRevD.104.083528

    doi:10.1103/physrevd.104.083528 2021

  22. [22]

    Q., & Gair, J

    Cheng, A. Q., & Gair, J. 2026, A unified harmonic framework for dark siren cosmology,https://arxiv.org/abs/2603. 13053

    2026

  23. [23]

    Cornish, N. J. 2010, Fast Fisher Matrices and Lazy Likelihoods, https://arxiv.org/abs/1007.4820

    Pith/arXiv arXiv 2010

  24. [24]

    K.-W., et al

    Cousins, B., Schumacher, K., Chung, A. K.-W., et al. 2025, The Stochastic Siren: Astrophysical Gravitational-Wave Back- ground Measurements of the Hubble Constant,https:// arxiv.org/abs/2503.01997

    arXiv 2025

  25. [25]

    L., Howlett, C., Davis, T

    Cross-Parkin, M. L., Howlett, C., Davis, T. M., & Khetan, N. 2025, Dark sirens and the impact of redshift precision, arXiv, doi:10.48550/arXiv.2502.17747

    doi:10.48550/arxiv.2502.17747 2025

  26. [26]

    2018, GLADE: A galaxy catalogue for multimessenger searches in the advanced gravitational-wave detector era, Mon

    D ´alya, G., Galg ´oczi, G., Dobos, L., et al. 2018, GLADE: A galaxy catalogue for multimessenger searches in the advanced gravitational-wave detector era, Mon. Not. Roy. Astron. Soc., 479, 2374, doi:10.1093/mnras/sty1703

    doi:10.1093/mnras/sty1703 2018

  27. [27]

    2022, GLADE+ : an extended galaxy catalogue for multimessenger searches with advanced gravitational-wave detectors, Mon

    D ´alya, G., et al. 2022, GLADE+ : an extended galaxy catalogue for multimessenger searches with advanced gravitational-wave detectors, Mon. Not. Roy. Astron. Soc., 514, 1403, doi:10. 1093/mnras/stac1443

    2022

  28. [28]

    2026, Golden and Silver Dark Sirens for Pre- cise H0 Measurement with HETDEX, Astrophys

    Dang, Y., et al. 2026, Golden and Silver Dark Sirens for Pre- cise H0 Measurement with HETDEX, Astrophys. J., 1003, 122, doi:10.3847/1538-4357/ae6329

    work page doi:10.3847/1538-4357/ae6329 2026

  29. [30]

    S., Agertz, O., Berbel, A

    de Jong, R. S., Agertz, O., Berbel, A. A., et al. 2019, 4MOST: Project overview and information for the First Call for Proposals, The Messenger, 175, 3, doi:10.18727/0722-6691/5117

    doi:10.18727/0722-6691/5117 2019

  30. [31]

    2022, Cosmography with bright and Love sirens,https://arxiv

    Dhani, A., Borhanian, S., Gupta, A., & Sathyaprakash, B. 2022, Cosmography with bright and Love sirens,https://arxiv. org/abs/2212.13183

    Pith/arXiv arXiv 2022

  31. [32]

    2019, Planck evi- dence for a closed Universe and a possible crisis for cosmology, Nature Astron., 4, 196, doi:10.1038/s41550-019-0906-9

    Di Valentino, E., Melchiorri, A., & Silk, J. 2019, Planck evi- dence for a closed Universe and a possible crisis for cosmology, Nature Astron., 4, 196, doi:10.1038/s41550-019-0906-9

    doi:10.1038/s41550-019-0906-9 2019

  32. [33]

    2021, In the realm of the Hubble tension—a review of solutions, Class

    Di Valentino, E., Mena, O., Pan, S., et al. 2021, In the realm of the Hubble tension—a review of solutions, Class. Quant. Grav., 38, 153001, doi:10.1088/1361-6382/ac086d

    doi:10.1088/1361-6382/ac086d 2021

  33. [34]

    2025, The CosmoVerse White Paper: Addressing observational tensions in cosmology with system- atics and fundamental physics, Phys

    Di Valentino, E., et al. 2025, The CosmoVerse White Paper: Addressing observational tensions in cosmology with system- atics and fundamental physics, Phys. Dark Univ., 49, 101965, doi:10.1016/j.dark.2025.101965

    arXiv 2025

  34. [35]

    C., & Mukherjee, S

    Diaz, C. C., & Mukherjee, S. 2022, Mapping the cosmic ex- pansion history from LIGO-Virgo-KAGRA in synergy with DESI and SPHEREx, Mon. Not. Roy. Astron. Soc., 511, 2782, 9 doi:10.1093/mnras/stac208

    doi:10.1093/mnras/stac208 2022

  35. [36]

    A., Smith, A., Szewciw, A

    Dong-P ´aez, C. A., Smith, A., Szewciw, A. O., et al. 2024, The Uchuu-SDSS galaxy light-cones: a clustering, redshift space distortion and baryonic acoustic oscillation study, Mon. Not. R. Astron. Soc., 528, 7236, doi:10.1093/mnras/stae062

    work page doi:10.1093/mnras/stae062 2024

  36. [37]

    2016, IMACS User Manual,,https://www.lco

    Dressler, A. 2016, IMACS User Manual,,https://www.lco. cl/technical-documentation/imacs-user-manual/

    2016

  37. [38]

    2011, IMACS: The Inamori-Magellan Areal Camera and Spectrograph on Magellan-Baade, Publ

    Dressler, A., Bigelow, B., Hare, T., et al. 2011, IMACS: The Inamori-Magellan Areal Camera and Spectrograph on Magellan-Baade, Publ. Astron. Soc. Pac., 123, 288, doi:10. 1086/658908

    2011

  38. [39]

    M., & Holz, D

    Ezquiaga, J. M., & Holz, D. E. 2022, Spectral Sirens: Cos- mology from the Full Mass Distribution of Compact Binaries, Phys. Rev. Lett., 129, 061102, doi:10.1103/PhysRevLett. 129.061102

    doi:10.1103/physrevlett 2022

  39. [40]

    2019, A Standard Siren Measurement of the Hubble Constant from GW170817 without the Electromag- netic Counterpart, Astrophys

    Fishbach, M., et al. 2019, A Standard Siren Measurement of the Hubble Constant from GW170817 without the Electromag- netic Counterpart, Astrophys. J. Lett., 871, L13, doi:10.3847/ 2041-8213/aaf96e

    2019

  40. [42]

    2021, The Hobby-Eberly Telescope Dark Energy Experiment (HET- DEX) Survey Design, Reductions, and Detections, Astrophys

    Gebhardt, K., Mentuch Cooper, E., Ciardullo, R., et al. 2021, The Hobby-Eberly Telescope Dark Energy Experiment (HET- DEX) Survey Design, Reductions, and Detections, Astrophys. J., 923, 217, doi:10.3847/1538-4357/ac2e03

    doi:10.3847/1538-4357/ac2e03 2021

  41. [43]

    Ghosh, T., & More, S. 2025, Constraining the Hubble Con- stant using Cross-Correlation of Gravitational Wave Events with Flux-Limited Galaxy Catalog, in 24th International Con- ference on General Relativity and Gravitation (GR24) and 16th Edoardo Amaldi Conference on Gravitational (Amaldi16) Waves.https://arxiv.org/abs/2510.22187

    arXiv 2025

  42. [44]

    2025, Bayesian frame- work to infer the Hubble constant from the cross-correlation of individual gravitational wave events with galaxies, Phys

    Ghosh, T., More, S., Bera, S., & Bose, S. 2025, Bayesian frame- work to infer the Hubble constant from the cross-correlation of individual gravitational wave events with galaxies, Phys. Rev. D, 111, 063513, doi:10.1103/PhysRevD.111.063513

    doi:10.1103/physrevd.111.063513 2025

  43. [45]

    Gray, R. 2021, Gravitational Wave Cosmology: Measuring the Hubble Constant with Dark Standard Sirens, Phd thesis, University of Glasgow, Glasgow, United Kingdom.https: //theses.gla.ac.uk/82438/

    2021

  44. [46]

    2020, Cosmological inference using gravitational wave standard sirens: A mock data analysis, Phys

    Gray, R., et al. 2020, Cosmological inference using gravitational wave standard sirens: A mock data analysis, Phys. Rev. D, 101, 122001, doi:10.1103/PhysRevD.101.122001

    doi:10.1103/physrevd.101.122001 2020

  45. [47]

    2023, Joint cosmological and gravitational-wave population inference using dark sirens and galaxy catalogues, JCAP, 12, 023, doi:10.1088/1475-7516/2023/12/023

    Gray, R., et al. 2023, Joint cosmological and gravitational-wave population inference using dark sirens and galaxy catalogues, JCAP, 12, 023, doi:10.1088/1475-7516/2023/12/023

    doi:10.1088/1475-7516/2023/12/023 2023

  46. [48]

    2023, Using grey sirens to resolve the Hub- ble–Lemaˆıtre tension, Mon

    Gupta, I. 2023, Using grey sirens to resolve the Hub- ble–Lemaˆıtre tension, Mon. Not. R. Astron. Soc., 524, 3537, doi:10.1093/mnras/stad2115

    doi:10.1093/mnras/stad2115 2023

  47. [49]

    2023, The DESI Bright Galaxy Survey: Final Target Selection, Design, and Validation, Astron

    Hahn, C., et al. 2023, The DESI Bright Galaxy Survey: Final Target Selection, Design, and Validation, Astron. J., 165, 253, doi:10.3847/1538-3881/accff8

    doi:10.3847/1538-3881/accff8 2023

  48. [50]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Array programming with NumPy, Nature, 585, 357–362, doi:10.1038/s41586-020-2649-2

    doi:10.1038/s41586-020-2649-2 2020

  49. [51]

    J., Lee, H., MacQueen, P

    Hill, G. J., Lee, H., MacQueen, P. J., et al. 2021, The HETDEX Instrumentation: Hobby-Eberly Telescope Wide-field Upgrade and VIRUS, Astron. J., 162, 298, doi:10.3847/1538-3881/ ac2c02

    doi:10.3847/1538-3881/ 2021

  50. [52]

    Accessed June 27, 2026, Tiling VIRUS Observations for Mapping Contiguous Areas,https: //hydra.as.utexas.edu/?a=help&h=138

    Hobby–Eberly Telescope. Accessed June 27, 2026, Tiling VIRUS Observations for Mapping Contiguous Areas,https: //hydra.as.utexas.edu/?a=help&h=138

    2026

  51. [53]

    E., & Hughes, S

    Holz, D. E., & Hughes, S. A. 2005, Using gravitational-wave standard sirens, Astrophys. J., 629, 15, doi:10.1086/431341

    doi:10.1086/431341 2005

  52. [54]

    Hunter, J. D. 2007, Matplotlib: A 2D Graphics Environment, Computing in Science and Engineering, 9, 90, doi:10.1109/ MCSE.2007.55

    2007

  53. [55]

    A., et al

    Ishiyama, T., Prada, F., Klypin, A. A., et al. 2021, The Uchuu simulations: Data Release 1 and dark matter halo concentra- tions, Mon. Not. R. Astron. Soc., 506, 4210, doi:10.1093/ mnras/stab1755

    2021

  54. [56]

    2023, Ac- celerated parameter estimation in Bilby with relative binning, https://arxiv.org/abs/2312.06009

    Krishna, K., Vijaykumar, A., Ganguly, A., et al. 2023, Ac- celerated parameter estimation in Bilby with relative binning, https://arxiv.org/abs/2312.06009

    Pith/arXiv arXiv 2023

  55. [57]

    2023, A# Strain Sensitiv- ity, Technical Notes, LIGO-T2300041,,https://dcc

    Kuns, K., & Fritschel, P. 2023, A# Strain Sensitiv- ity, Technical Notes, LIGO-T2300041,,https://dcc. ligo.org/LIGO-T2300041/public https://dcc.ligo. org/LIGO-T2300041/public

    2023

  56. [58]

    J., Cannon, R

    Lewis, I. J., Cannon, R. D., Taylor, K., et al. 2002, The Anglo- Australian Observatory 2dF facility, Mon. Not. R. Astron. Soc., 333, 279, doi:10.1046/j.1365-8711.2002.05333.x

    arXiv 2002

  57. [59]

    2014, Cosmic Star-Formation His- tory, Annu

    Madau, P., & Dickinson, M. 2014, Cosmic Star-Formation His- tory, Annu. Rev. Astron. Astrophys., 52, 415, doi:10.1146/ annurev-astro-081811-125615

    2014

  58. [60]

    2016, The New Numerical Galaxy Catalog (𝜈 2GC): An updated semi-analytic model of galaxy and active galactic nucleus formation with large cosmological N-body simulations, Publ

    Makiya, R., Enoki, M., Ishiyama, T., et al. 2016, The New Numerical Galaxy Catalog (𝜈 2GC): An updated semi-analytic model of galaxy and active galactic nucleus formation with large cosmological N-body simulations, Publ. Astron. Soc. Jpn., 68, 25, doi:10.1093/pasj/psw005

    work page doi:10.1093/pasj/psw005 2016

  59. [61]

    2025, Striking a Chord with Spec- tral Sirens: Multiple Features in the Compact Binary Popu- lation Correlate with H0, Astrophys

    Mali, U., & Essick, R. 2025, Striking a Chord with Spec- tral Sirens: Multiple Features in the Compact Binary Popu- lation Correlate with H0, Astrophys. J., 980, 85, doi:10.3847/ 1538-4357/ad9de7

    2025

  60. [62]

    2021, On the importance of source population models for gravitational- wave cosmology, Phys

    Mastrogiovanni, S., Leyde, K., Karathanasis, C., et al. 2021, On the importance of source population models for gravitational- wave cosmology, Phys. Rev. D, 104, 062009, doi:10.1103/ PhysRevD.104.062009

    2021

  61. [63]

    McMahon, I., et al. 2026, Measurement of the Hubble con- stant using the Dark Energy Survey Year 6 Gold galaxy catalog and the fourth Gravitational-Wave Transient Catalog,https: //arxiv.org/abs/2602.04766

    Pith/arXiv arXiv 2026

  62. [64]

    2012, Measuring a cosmological distance-redshift relationship using only gravitational wave ob- servations of binary neutron star coalescences, Phys

    Messenger, C., & Read, J. 2012, Measuring a cosmological distance-redshift relationship using only gravitational wave ob- servations of binary neutron star coalescences, Phys. Rev. Lett., 108, 091101, doi:10.1103/PhysRevLett.108.091101

    doi:10.1103/physrevlett.108.091101 2012

  63. [65]

    2022, The redshift dependence of black hole mass distribution: is it reliable for standard sirens cosmology?, Mon

    Mukherjee, S. 2022, The redshift dependence of black hole mass distribution: is it reliable for standard sirens cosmology?, Mon. Not. Roy. Astron. Soc., 515, 5495, doi:10.1093/mnras/ stac2152

    doi:10.1093/mnras/ 2022

  64. [66]

    D., & Silk, J

    Mukherjee, S., Krolewski, A., Wandelt, B. D., & Silk, J. 2024, Cross-correlating dark sirens and galaxies: constraints on𝐻 0 from GWTC-3 of LIGO-Virgo-KAGRA, Astrophys. J., 975, 189, doi:10.3847/1538-4357/ad7d90

    doi:10.3847/1538-4357/ad7d90 2024

  65. [67]

    D., Nissanke, S

    Mukherjee, S., Wandelt, B. D., Nissanke, S. M., & Silvestri, A. 2021, Accurate precision Cosmology with redshift unknown gravitational wave sources, Phys. Rev. D, 103, 043520, doi:10. 1103/PhysRevD.103.043520

    2021

  66. [68]

    D., & Silk, J

    Mukherjee, S., Wandelt, B. D., & Silk, J. 2020, Probing the the- ory of gravity with gravitational lensing of gravitational waves and galaxy surveys, Mon. Not. Roy. Astron. Soc., 494, 1956, doi:10.1093/mnras/staa827

    doi:10.1093/mnras/staa827 2020

  67. [69]

    2016, Anisotropies of gravitational-wave standard sirens as a new cosmologi- cal probe without redshift information, Phys

    Namikawa, T., Nishizawa, A., & Taruya, A. 2016, Anisotropies of gravitational-wave standard sirens as a new cosmologi- cal probe without redshift information, Phys. Rev. Lett., 116, 121302, doi:10.1103/PhysRevLett.116.121302

    doi:10.1103/physrevlett.116.121302 2016

  68. [70]

    Ng, K. K. Y., Vitale, S., Farr, W. M., & Rodriguez, C. L. 2021, Probing multiple populations of compact binaries with third- 10 generation gravitational-wave detectors, Astrophys. J. Lett., 913, L5, doi:10.3847/2041-8213/abf8be

    doi:10.3847/2041-8213/abf8be 2021

  69. [71]

    2023, Uchuu-𝜈 2GC galaxies and AGN: cosmic variance forecasts of high-redshift AGN for JWST, Euclid, and LSST, Mon

    Oogi, T., Ishiyama, T., Prada, F., et al. 2023, Uchuu-𝜈 2GC galaxies and AGN: cosmic variance forecasts of high-redshift AGN for JWST, Euclid, and LSST, Mon. Not. R. Astron. Soc., 525, 3879, doi:10.1093/mnras/stad2401

    doi:10.1093/mnras/stad2401 2023

  70. [72]

    R., Mucesh, S., & Hartley, W

    Palmese, A., Bom, C. R., Mucesh, S., & Hartley, W. G. 2023, A Standard Siren Measurement of the Hubble Constant Using Gravitational-wave Events from the First Three LIGO/Virgo Observing Runs and the DESI Legacy Survey, Astrophys. J., 943, 56, doi:10.3847/1538-4357/aca6e3

    doi:10.3847/1538-4357/aca6e3 2023

  71. [73]

    2024, Standard siren measurement of the Hubble constant using GW170817 and the latest observations of the electromagnetic counterpart afterglow, Phys

    Palmese, A., Kaur, R., Hajela, A., et al. 2024, Standard siren measurement of the Hubble constant using GW170817 and the latest observations of the electromagnetic counterpart afterglow, Phys. Rev. D, 109, 063508, doi:10.1103/PhysRevD.109. 063508

    doi:10.1103/physrevd.109 2024

  72. [74]

    2026, Gravitational wave cosmology, in Encyclopedia of Astrophysics, Volume 5, Vol

    Palmese, A., & Mastrogiovanni, S. 2026, Gravitational wave cosmology, in Encyclopedia of Astrophysics, Volume 5, Vol. 5, 557–576, doi:10.1016/B978-0-443-21439-4.00107-3

    doi:10.1016/b978-0-443-21439-4.00107-3 2026

  73. [75]

    Palmese, A., et al. 2020, A statistical standard siren measure- ment of the Hubble constant from the LIGO/Virgo gravitational wave compact object merger GW190814 and Dark Energy Sur- vey galaxies, Astrophys. J. Lett., 900, L33, doi:10.3847/ 2041-8213/abaeff

    2020

  74. [76]

    L., Karwal, T., & Kamionkowski, M

    Poulin, V., Smith, T. L., Karwal, T., & Kamionkowski, M. 2019, Early Dark Energy Can Resolve The Hubble Tension, Phys. Rev. Lett., 122, 221301, doi:10.1103/PhysRevLett.122.221301

    doi:10.1103/physrevlett.122.221301 2019

  75. [77]

    2021, Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys

    Pratten, G., et al. 2021, Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes, Phys. Rev. D, 103, 104056, doi:10.1103/ PhysRevD.103.104056

    2021

  76. [78]

    M., Sip ˝ocz, B

    Price-Whelan, A. M., Sip ˝ocz, B. M., G¨ unther, H. M., et al. 2018, The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package*, The Astronomical Journal, 156, 123, doi:10.3847/1538-3881/aabc4f

    doi:10.3847/1538-3881/aabc4f 2018

  77. [79]

    W., Adams, M

    Ramsey, L. W., Adams, M. T., Barnes, T. G., et al. 1998, Early performance and present status of the Hobby-Eberly Telescope, in Society of Photo-Optical Instrumentation Engi- neers (SPIE) Conference Series, Vol. 3352, Advanced Tech- nology Optical/IR Telescopes VI, ed. L. M. Stepp, 34–42, doi:10.1117/12.319287

    doi:10.1117/12.319287 1998

  78. [80]

    G., et al

    Riess, A. G., et al. 2022, A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team, Astrophys. J. Lett., 934, L7, doi:10.3847/2041-8213/ ac5c5b

    doi:10.3847/2041-8213/ 2022

  79. [81]

    G., Li, S., Anand, G

    Riess, A. G., Li, S., Anand, G. S., et al. 2025, The Per- fect Host: JWST Cepheid Observations in a Background-free Type Ia Supernova Host Confirm No Bias in Hubble-constant Measurements, Astrophys. J. Lett., 992, L34, doi:10.3847/ 2041-8213/ae0ad6

    2025

  80. [82]

    Schutz, B. F. 1986, Determining the Hubble Constant from Gravitational Wave Observations, Nature (London), 323, 310, doi:10.1038/323310a0

    doi:10.1038/323310a0 1986

Showing first 80 references.