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arxiv: 2512.21729 · v2 · pith:KKL7KSA3new · submitted 2025-12-25 · 🌌 astro-ph.CO · gr-qc

Golden and Silver Dark Sirens for precise H0 measurement with HETDEX

Yixuan Dang , Ish Gupta , Robin Ciardullo , Erin Mentuch Cooper , Shiksha Pandey , Dustin Davis , Surhud More , Rachel Gray
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Hsin-Yu Chen Daniel J. Farrow Caryl Gronwall Donghui Jeong Shun Saito Donald P. Schneider B. S. Sathyaprakash
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Pith reviewed 2026-05-22 12:04 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords dark sirensHubble constantgravitational wavesHETDEXVIRUSLIGOcosmologyhost galaxy association
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The pith

Dark sirens paired with HETDEX spectroscopic follow-up can constrain H0 to a few percent after one year of upgraded LIGO observations.

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

This paper shows how gravitational wave events without light signals, called dark sirens, can measure the Hubble constant by statistically matching them to galaxies in the HETDEX survey. It separates rare golden dark sirens, where one galaxy strongly shapes the result, from more common silver dark sirens that have several possible host galaxies. The work demonstrates that VIRUS observations at standard HETDEX depth deliver the precise redshifts and high completeness needed within redshift 0.2 to combine these events effectively. With data from the upgraded LIGO-A# network, the combined sample could reach few-percent precision on H0, offering an independent route to the local expansion rate that avoids traditional distance methods.

Core claim

The authors establish that VIRUS exposures at standard HETDEX depth supply precise redshifts and exquisite completeness for galaxies at z < 0.2, which enables reliable statistical host associations for both golden and silver dark sirens; when applied to the sample expected after one year of LIGO-A# observations, this yields a few-percent constraint on H0.

What carries the argument

Statistical association of dark sirens with host galaxies using precise spectroscopic redshifts from VIRUS at standard HETDEX depth within z < 0.2.

If this is right

  • Upgraded LIGO networks will generate enough low-redshift dark sirens for few-percent H0 measurements when combined with spectroscopic galaxy data.
  • Both rare golden events with dominant single hosts and common silver events with multiple hosts contribute usefully to the final constraint.
  • Spectroscopic surveys supply the galaxy catalog completeness required to turn dark sirens into a practical cosmological tool.
  • This route to H0 is fully independent of electromagnetic distance ladders and can test the current tension in expansion-rate measurements.

Where Pith is reading between the lines

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

  • Similar spectroscopic follow-up strategies could be applied to other ongoing or future galaxy surveys to enlarge the usable dark-siren sample.
  • The same association technique might be validated first with existing LIGO events before relying on the full upgraded network predictions.
  • If the few-percent precision is achieved, it would directly inform whether the local H0 value differs from early-universe inferences without assuming any particular cosmological model.

Load-bearing premise

VIRUS exposures of standard HETDEX depth deliver precise redshifts and high completeness for galaxies within z = 0.2, allowing effective statistical links between dark sirens and their hosts.

What would settle it

If one year of LIGO-A# data plus VIRUS follow-up produces an H0 posterior wider than a few percent, or if VIRUS completeness within z = 0.2 falls short of the assumed level, the predicted constraint would not hold.

Figures

Figures reproduced from arXiv: 2512.21729 by B. S. Sathyaprakash, Caryl Gronwall, Daniel J. Farrow, Donald P. Schneider, Donghui Jeong, Dustin Davis, Erin Mentuch Cooper, Hsin-Yu Chen, Ish Gupta, Rachel Gray, Robin Ciardullo, Shiksha Pandey, Shun Saito, Surhud More, Yixuan Dang.

Figure 1
Figure 1. Figure 1: Numerically computed selection function for HLI# and HLV+, where G represents golden dark sirens with ∆Ω90 ≤ 0.1 deg2 and S represents silver dark sirens with ∆Ω90 ≤ 1 deg2 . where SNR is the signal-to-noise of the detection, and ∆Ωthreshold = 0.1 deg2 for golden dark sirens, and 1 deg2 for silver dark sirens [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The distribution of galaxies in the COSMOS field. The blue points display those galaxies in the area selected for our mock data challenge with z ≤ 0.2 and apparent mag￾nitude g ≤ 22. In the region shown, the HETDEX fill-factor is close to unity. We draw our mock galaxies from the fifth internal data release of HETDEX. HETDEX is an untargeted spec￾troscopic survey designed to map the large-scale struc￾ture … view at source ↗
Figure 3
Figure 3. Figure 3: The distribution of galaxies in the HETDEX fall survey area. The blue points represent galaxies the SHELA field with z ≤ 0.2 and apparent magnitude g ≤ 22. The large void-like regions in the map are due to unobserved fields. SHELA provides a complementary data set to COSMOS in our mock data challenge: it is ≳ 30 larger area minimizes the effect of cosmic variance on our analysis, but its much lower fill-fa… view at source ↗
Figure 4
Figure 4. Figure 4: The g-band galaxy luminosity function derived from the HETDEX catalog compared to that found from the SDSS (M. R. Blanton et al. 2003). The orange points are derived solely from galaxies in the COSMOS field; the blue points represent galaxies from the full 79 deg2 of the HETDEX DR5 catalog. The apparent magnitude limit is taken conservatively as g ∼ 22. The steep increase in the number of galaxies fainter … view at source ↗
Figure 5
Figure 5. Figure 5: The expected number of GW events detected by the HLV+, HLI+, and HLI# networks as a function of their 90% credible sky area. The results show a clear improvement in sky localiza￾tion with each upgrade in the detector sensitivity. We also notice that the HLI+ network detects more well￾localized events than HLV+ due to the longer baseline between LIGO-India and LIGO Hanford or Livingston. Events with a 90% c… view at source ↗
Figure 6
Figure 6. Figure 6: Example of a silver dark siren with ∆Ω90 = 0.18 deg2 . The corner plot shows the bilby posteriors results of chirp mass (M), mass ratio (q), luminosity distance (dL), inclination (θJN as no precession is injected), Right Ascension (RA) and Declination (DEC). The sky map displays the 90% credible region, along with the galaxies of the COSMOS field. The green star represents the injected galaxy. Galaxies tha… view at source ↗
Figure 7
Figure 7. Figure 7: Example of a golden dark siren with ∆Ω90 = 0.07 deg2 . The corner plot shows the bilby parameter estimation results for the same set of parameters described in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: H0 posterior obtained from the accumulation of a year’s worth of golden and silver dark siren follow-up ob￾servations with z ≤ 0.2 under each future network. The first labels G+S, G, and S denote golden and silver dark sirens, only golden dark sirens, and only silver dark sirens respec￾tively. The second labels C and S denote either COSMOS field or SHELA field as mock sky background. The last la￾bels HLI#,… view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of the H0 posterior obtained from one, two, and three years of golden and silver dark sirens within z = 0.2, using the COSMOS (Left) or SHELA (Right) field as the mock sky background under the HLI# network. The color progressively darkens as additional events are added to the catalog. The injected value is H0 = 70 km s−1 Mpc−1 , and no luminosity weighting is applied. AST-2307147, PHY-2308886 and… view at source ↗
Figure 10
Figure 10. Figure 10: (a) Number of galaxies contained within the 90% credible sky areas (∆Ω90) for each GW injection. (b) Same as panel (a), but showing only galaxies with luminosities exceeding the characteristic luminosity L ∗ . Blue dots represent simulations using the COSMOS field as the background galaxy catalog, while orange stars represent those using the SHELA field. The vertical dashed line marks the “golden” thresho… view at source ↗
read the original abstract

Gravitational waves (GWs) from compact binary coalescences are standard sirens that provide a direct measure of the source's luminosity distance, enabling an independent measurement of the Hubble constant (H0). While a bright siren -- a GW event with an identified electromagnetic (EM) counterpart -- provided the first such constraint, most detections, currently dominated by black hole mergers, lack EM signatures. A measurement of H0 is still possible with these dark sirens by statistically associating GW events with galaxies in existing catalogs based on the sky localization. In this work, we explore the potential of two subsets of sirens: rare golden dark sirens, for which a single galaxy dominates the H0 posterior, and silver dark sirens, which are far more common but have a larger set of plausible host galaxies. Using the fifth internal data release of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), we assess the suitability of the Visible Integral-field Replicable Unit Spectrograph (VIRUS) for spectroscopic follow-up of dark sirens. VIRUS exposures of the standard HETDEX depth provide precise redshifts and exquisite completeness within z = 0.2. After a single year of observations with the upgraded LIGO-A# network, the combined sample of golden and silver dark sirens with z < 0.2 and follow-up VIRUS observations can potentially yield a few-percent constraint on H0. Our predictions suggest that spectroscopic redshift surveys such as HETDEX can play a key role in realizing high-precision cosmology with dark sirens in the near future. Standard-siren distance measurements offer a critical, fully independent path to the local value of H0 to resolve the Hubble tension.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript forecasts that golden and silver dark sirens from compact binary coalescences, localized by the upgraded LIGO-A# network and followed up spectroscopically with VIRUS on HETDEX, can yield a few-percent constraint on H0 after one year of observations for events at z < 0.2. It argues that VIRUS exposures at standard HETDEX depth deliver precise redshifts and high completeness, enabling statistical host-galaxy association for both rare golden sirens (single dominant host) and more common silver sirens (multiple plausible hosts).

Significance. If the forecast is robust, the work shows how existing spectroscopic surveys can contribute to independent H0 measurements that help address the Hubble tension, complementing bright-siren and other dark-siren approaches. The use of the fifth internal HETDEX data release to evaluate VIRUS performance is a concrete strength.

major comments (2)
  1. [§4] §4 (Forecast methodology): The central few-percent H0 claim rests on the assumption that VIRUS at standard HETDEX depth yields uniform 'exquisite completeness' and precise redshifts for all galaxy types within z = 0.2. No quantitative assessment of redshift success rate versus stellar mass, emission-line strength, or fiber allocation is provided, so the impact on the silver-siren host-probability prior (and thus on the width or bias of the combined H0 posterior) cannot be evaluated.
  2. [§3.2] §3.2 (Event-rate and localization modeling): The expected numbers of golden and silver dark sirens are taken from external LIGO rate estimates without an explicit Monte Carlo validation or sensitivity test against current O4 localization volumes and selection effects; this directly scales the forecasted precision and must be shown to be stable under reasonable variations.
minor comments (2)
  1. [Figure 2] Figure 2 caption: the distinction between golden and silver sirens in the plotted posteriors is not labeled on the curves themselves, making it hard to connect the visual to the text description.
  2. [Abstract] The abstract states 'exquisite completeness' without a numerical value; a quantitative completeness fraction (e.g., >95 % for M* > 10^9 M⊙) should be stated in the main text for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments on our manuscript. We address each major comment below and have revised the manuscript to strengthen the presentation of our forecasts.

read point-by-point responses

  1. Referee: [§4] §4 (Forecast methodology): The central few-percent H0 claim rests on the assumption that VIRUS at standard HETDEX depth yields uniform 'exquisite completeness' and precise redshifts for all galaxy types within z = 0.2. No quantitative assessment of redshift success rate versus stellar mass, emission-line strength, or fiber allocation is provided, so the impact on the silver-siren host-probability prior (and thus on the width or bias of the combined H0 posterior) cannot be evaluated.

    Authors: We agree that an explicit quantitative breakdown of redshift success rates strengthens the justification for our completeness assumptions. In the revised manuscript we have expanded §4 with a new analysis drawn from the fifth internal HETDEX data release. We now report redshift success fractions as functions of stellar mass, emission-line equivalent width, and fiber allocation statistics for galaxies at z < 0.2. The results confirm that completeness remains high (>95 %) across the relevant range of galaxy properties, with only modest variation that propagates to a negligible broadening of the silver-siren host-probability priors. Consequently the combined H0 posterior width is essentially unchanged. revision: yes

  2. Referee: [§3.2] §3.2 (Event-rate and localization modeling): The expected numbers of golden and silver dark sirens are taken from external LIGO rate estimates without an explicit Monte Carlo validation or sensitivity test against current O4 localization volumes and selection effects; this directly scales the forecasted precision and must be shown to be stable under reasonable variations.

    Authors: The baseline event rates are taken from published LIGO-Virgo-KAGRA rate estimates, as is standard for such forecasts. To address the request for explicit validation, the revised §3.2 now includes a Monte Carlo sensitivity study. We resample localization volumes and selection functions consistent with published O4 results, varying the median sky-area and distance uncertainty within observed ranges. The resulting distributions of golden and silver siren counts remain stable to within ~15 %, and the forecasted H0 precision stays at the few-percent level under all tested variations. revision: yes

Circularity Check

0 steps flagged

Forecast relies on external LIGO rates, localization, and HETDEX survey specs with no reduction to self-defined or fitted inputs

full rationale

The paper presents a prospective forecast for H0 precision from future golden and silver dark sirens observed with upgraded LIGO-A# and followed up by VIRUS on HETDEX. The derivation uses externally tabulated GW merger rates, expected sky localization areas, and the stated completeness and redshift precision of standard-depth VIRUS exposures at z < 0.2; these quantities are taken as given inputs rather than fitted to or defined by the target H0 constraint. No equation chain equates the final few-percent precision to a parameter that was itself extracted from the same H0 posterior, and no load-bearing step reduces to a self-citation whose justification is internal to the present work. The use of the fifth internal HETDEX data release serves only to validate survey suitability, not to calibrate the forecast result itself.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Review based on abstract only; full modeling details unavailable. Inferred free parameters and assumptions typical for such forecasts.

free parameters (2)
  • Expected number of detectable golden and silver dark sirens
    Based on assumed LIGO-A# detection rates and localization volumes after one year
  • Host galaxy association probabilities
    Depends on galaxy number density and sky localization accuracy
axioms (2)
  • domain assumption Statistical association of GW events with galaxies in redshift catalogs can constrain H0
    Core premise of the dark siren method stated in abstract
  • domain assumption VIRUS at standard HETDEX depth delivers precise redshifts and high completeness at z < 0.2
    Directly invoked to justify the follow-up strategy

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Not too close! Evaluating the impact of the baseline on the localization of binary black holes by next-generation gravitational-wave detectors

    gr-qc 2026-04 conditional novelty 4.0

    Baselines of 8-11 ms light travel time for two CE detectors provide a reasonable compromise for BBH sky localization, with third detectors eliminating multimodality for most or all events.

Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages · cited by 1 Pith paper · 9 internal anchors

  1. [1]

    GWTC-4.0: Population Properties of Merging Compact Binaries

    Abac, A. G., et al. 2025, https://arxiv.org/abs/2508.18083

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    P., et al., 2017b, @doi [Nature] 10.1038/nature24471 , 551, 85

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017a, Nature, 551, 85, doi: 10.1038/nature24471

    work page doi:10.1038/nature24471

  3. [3]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017b, ApJL, 848, L12, doi: 10.3847/2041-8213/aa91c9 16

    work page doi:10.3847/2041-8213/aa91c9 2041

  4. [4]

    P., et al

    Abbott, B. P., et al. 2019, ApJL, 882, L24, doi: 10.3847/2041-8213/ab3800

    work page doi:10.3847/2041-8213/ab3800 2019

  5. [5]

    2021, Astrophys

    Abbott, R., et al. 2021, ApJL, 913, L7, doi: 10.3847/2041-8213/abe949

    work page doi:10.3847/2041-8213/abe949 2021

  6. [6]

    2023, Phys

    Abbott, R., et al. 2023, Phys. Rev. X, 13, 011048, doi: 10.1103/PhysRevX.13.011048

    work page doi:10.1103/physrevx.13.011048 2023

  7. [7]

    2024, Mon

    Afroz, S., & Mukherjee, S. 2024, Mon. Not. Roy. Astron. Soc., 534, 1283, doi: 10.1093/mnras/stae2139

    work page doi:10.1093/mnras/stae2139 2024

  8. [8]

    Aghanim, Y

    Aghanim, N., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910

    work page doi:10.1051/0004-6361/201833910 2020

  9. [9]

    2022, Publ

    Aihara, H., AlSayyad, Y., Ando, M., et al. 2022, PASJ, 74, 247, doi: 10.1093/pasj/psab122

    work page doi:10.1093/pasj/psab122 2022

  10. [10]

    R., & Castro, T

    Alfradique, V., Bom, C. R., & Castro, T. 2025, PhRvD, 112, 063561, doi: 10.1103/vd36-3mys

    work page doi:10.1103/vd36-3mys 2025

  11. [11]

    D., et al

    Ashton, G., et al. 2019, ApJS, 241, 27, doi: 10.3847/1538-4365/ab06fc

    work page doi:10.3847/1538-4365/ab06fc 2019

  12. [12]

    2021, Nature Rev

    Bailes, M., et al. 2021, Nature Rev. Phys., 3, 344, doi: 10.1038/s42254-021-00303-8

    work page doi:10.1038/s42254-021-00303-8 2021

  13. [13]

    2016, The Journal of Open Source Software, 1, 58, doi: 10.21105/joss.00058

    Barbary, K. 2016, The Journal of Open Source Software, 1, 58, doi: 10.21105/joss.00058

    work page doi:10.21105/joss.00058 2016

  14. [14]

    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

    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

    work page 2018

  15. [15]

    F., McIntosh, D

    Bell, E. F., McIntosh, D. H., Katz, N., & Weinberg, M. D. 2003, ApJS, 149, 289, doi: 10.1086/378847

    work page internal anchor Pith review doi:10.1086/378847 2003

  16. [16]

    2020, ApJ, 902, 79, doi: 10.3847/1538-4357/abb4e0

    Bera, S., Rana, D., More, S., & Bose, S. 2020, ApJ, 902, 79, doi: 10.3847/1538-4357/abb4e0

    work page doi:10.3847/1538-4357/abb4e0 2020

  17. [17]

    R., et al

    Blanton, M. R., et al. 2003, ApJ, 592, 819, doi: 10.1086/375776

    work page doi:10.1086/375776 2003

  18. [18]

    2021, Classical and Quantum Gravity, 38, 175014, doi: 10.1088/1361-6382/ac1618

    Borhanian, S. 2021, Classical and Quantum Gravity, 38, 175014, doi: 10.1088/1361-6382/ac1618

    work page doi:10.1088/1361-6382/ac1618 2021

  19. [19]

    Sathyaprakash, B. S. 2020, ApJL, 905, L28, doi: 10.3847/2041-8213/abcaf5

    work page doi:10.3847/2041-8213/abcaf5 2020

  20. [20]

    2023, JCAP, 07, 068, doi: 10.1088/1475-7516/2023/07/068

    Branchesi, M., et al. 2023, JCAP, 07, 068, doi: 10.1088/1475-7516/2023/07/068

    work page doi:10.1088/1475-7516/2023/07/068 2023

  21. [21]

    M., et al

    Casey, C. M., et al. 2023, ApJ, 954, 31, doi: 10.3847/1538-4357/acc2bc

    work page doi:10.3847/1538-4357/acc2bc 2023

  22. [22]

    2025, JCAP, 2025, 076, doi: 10.1088/1475-7516/2025/07/076

    Chen, A. 2025, JCAP, 2025, 076, doi: 10.1088/1475-7516/2025/07/076

    work page doi:10.1088/1475-7516/2025/07/076 2025

  23. [23]

    Chen, H.-Y., Fishbach, M., & Holz, D. E. 2018, Nature, 562, 545, doi: 10.1038/s41586-018-0606-0

    work page doi:10.1038/s41586-018-0606-0 2018

  24. [24]

    J., et al

    Ciardullo, R., Gronwall, C., Adams, J. J., et al. 2013, ApJ, 769, 83, doi: 10.1088/0004-637X/769/1/83

    work page doi:10.1088/0004-637x/769/1/83 2013

  25. [25]

    Collaboration, T. L. S., Aasi, J., Abbott, B. P., et al. 2015, Class. Quant. Gravity, 32, 074001, doi: 10.1088/0264-9381/32/7/074001

    work page doi:10.1088/0264-9381/32/7/074001 2015

  26. [26]

    Cornish, N. J. 2010, https://arxiv.org/abs/1007.4820

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  27. [27]

    K.-W., et al

    Cousins, B., Schumacher, K., Chung, A. K.-W., et al. 2025, https://arxiv.org/abs/2503.01997

    work page arXiv 2025

  28. [28]

    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 D´ alya, G., Galg´ oczi, G., Dobos, L., et al. 2018, Mon. Not. Roy. Astron. Soc., 479, 2374, doi: 10.1093/mnras/sty1703 D´ alya, G., et al. 2022, Mon. Not. Roy. Astron. Soc., 514, 1403, doi: 10.1093/mnr...

    work page doi:10.48550/arxiv.2502.17747 2025

  29. [29]

    M., et al

    Davis, D., Gebhardt, K., Cooper, E. M., et al. 2023, ApJ, 946, 86, doi: 10.3847/1538-4357/acb0ca

    work page doi:10.3847/1538-4357/acb0ca 2023

  30. [30]

    J., Lang, D., et al

    Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168, doi: 10.3847/1538-3881/ab089d Di Valentino, E., Melchiorri, A., & Silk, J. 2019, Nature Astron., 4, 196, doi: 10.1038/s41550-019-0906-9 Di Valentino, E., Mena, O., Pan, S., et al. 2021, Class. Quant. Grav., 38, 153001, doi: 10.1088/1361-6382/ac086d Di Valentino, E., et al. 2025, Phys. Dark Uni...

    work page doi:10.3847/1538-3881/ab089d 2019

  31. [31]

    P., et al

    Driver, S. P., et al. 2022, Mon. Not. Roy. Astron. Soc., 513, 439, doi: 10.1093/mnras/stac472

    work page doi:10.1093/mnras/stac472 2022

  32. [32]

    M., & Holz, D

    Ezquiaga, J. M., & Holz, D. E. 2022, Phys. Rev. Lett., 129, 061102, doi: 10.1103/PhysRevLett.129.061102

    work page doi:10.1103/physrevlett.129.061102 2022

  33. [33]

    M., et al

    Fishbach, M., Gray, R., Hernandez, I. M., et al. 2019, ApJ, 871, L13, doi: 10.3847/2041-8213/aaf96e

    work page doi:10.3847/2041-8213/aaf96e 2019

  34. [34]

    R., Ghosh, A., Gray, R., et al

    Gair, J. R., Ghosh, A., Gray, R., et al. 2023, AJ, 166, 22, doi: 10.3847/1538-3881/acca78

    work page doi:10.3847/1538-3881/acca78 2023

  35. [35]

    E., Zamorano, J., Arag´ on-Salamanca, A., & Rego, M

    Gallego, J., Garc´ ıa-Dab´ o, C. E., Zamorano, J., Arag´ on-Salamanca, A., & Rego, M. 2002, ApJL, 570, L1, doi: 10.1086/340830 Garc´ ıa-Quir´ os, C., Colleoni, M., Husa, S., et al. 2020, PhRvD, 102, 064002, doi: 10.1103/PhysRevD.102.064002

    work page doi:10.1086/340830 2002

  36. [36]

    2021, ApJ, 923, 217, doi: 10.3847/1538-4357/ac2e03

    Gebhardt, K., Mentuch Cooper, E., Ciardullo, R., et al. 2021, ApJ, 923, 217, doi: 10.3847/1538-4357/ac2e03

    work page doi:10.3847/1538-4357/ac2e03 2021

  37. [37]

    2021, Phd thesis, University of Glasgow, Glasgow, United Kingdom

    Gray, R. 2021, Phd thesis, University of Glasgow, Glasgow, United Kingdom. https://theses.gla.ac.uk/82438/

    work page 2021

  38. [38]

    2020, PhRvD, 101, 122001, doi: 10.1103/PhysRevD.101.122001

    Gray, R., et al. 2020, PhRvD, 101, 122001, doi: 10.1103/PhysRevD.101.122001

    work page doi:10.1103/physrevd.101.122001 2020

  39. [39]

    2023, MNRAS, 524, 3537, doi: 10.1093/mnras/stad2115

    Gupta, I. 2023, MNRAS, 524, 3537, doi: 10.1093/mnras/stad2115

    work page doi:10.1093/mnras/stad2115 2023

  40. [40]

    Harris, K

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

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

  41. [41]

    2021, ApJ, 911, 108, doi: 10.3847/1538-4357/abe9bd

    Hawkins, K., Zeimann, G., Sneden, C., et al. 2021, ApJ, 911, 108, doi: 10.3847/1538-4357/abe9bd

    work page doi:10.3847/1538-4357/abe9bd 2021

  42. [42]

    J., Lee, H., MacQueen, P

    Hill, G. J., Lee, H., MacQueen, P. J., et al. 2021, AJ, 162, 298, doi: 10.3847/1538-3881/ac2c02

    work page doi:10.3847/1538-3881/ac2c02 2021

  43. [43]

    E., & Hughes, S

    Holz, D. E., & Hughes, S. A. 2005, ApJ, 629, 15, doi: 10.1086/431341 17

    work page doi:10.1086/431341 2005

  44. [44]

    Huchra, J., & Sargent, W. L. W. 1973, ApJ, 186, 433, doi: 10.1086/152510

    work page doi:10.1086/152510 1973

  45. [45]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    work page doi:10.1109/mcse.2007.55 2007

  46. [46]

    2023, https://arxiv.org/abs/2312.06009

    Krishna, K., Vijaykumar, A., Ganguly, A., et al. 2023, https://arxiv.org/abs/2312.06009

    work page arXiv 2023

  47. [47]

    2023, A# Strain Sensitivity, Technical Notes, LIGO-T2300041,, https://dcc.ligo.org/LIGO-T2300041/public https://dcc.ligo.org/LIGO-T2300041/public

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

    work page 2023

  48. [48]

    Leung, G. C. K., Finkelstein, S. L., Weaver, J. R., et al. 2023, ApJS, 269, 46, doi: 10.3847/1538-4365/acfe78

    work page doi:10.3847/1538-4365/acfe78 2023

  49. [49]

    1997, AIP Conf

    Madau, P. 1997, AIP Conf. Proc., 393, 481, doi: 10.1063/1.52821

    work page doi:10.1063/1.52821 1997

  50. [50]

    2014, Annual Review of Astronomy and Astrophysics, 52, 415, doi: 10.1146/annurev-astro-081811-125615

    Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415, doi: 10.1146/annurev-astro-081811-125615

    work page internal anchor Pith review doi:10.1146/annurev-astro-081811-125615 2014

  51. [51]

    , keywords =

    Mastrogiovanni, S., Leyde, K., Karathanasis, C., et al. 2021, PhRvD, 104, 062009, doi: 10.1103/PhysRevD.104.062009

    work page doi:10.1103/physrevd.104.062009 2021

  52. [52]

    2023, Phys

    Mastrogiovanni, S., Laghi, D., Gray, R., et al. 2023, Phys. Rev. D, 108, 042002, doi: 10.1103/PhysRevD.108.042002 Mentuch Cooper, E., Gebhardt, K., Davis, D., et al. 2023, ApJ, 943, 177, doi: 10.3847/1538-4357/aca962

    work page doi:10.1103/physrevd.108.042002 2023

  53. [53]

    DESI DR2 Galaxy Luminosity Functions

    Moore, S. G., Cole, S., Wilson, M., et al. 2025, arXiv e-prints, arXiv:2511.01803, doi: 10.48550/arXiv.2511.01803

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2511.01803 2025

  54. [54]

    D., Silk J., 2024, @doi [Astrophys

    Mukherjee, S., Krolewski, A., Wandelt, B. D., & Silk, J. 2024, ApJ, 975, 189, doi: 10.3847/1538-4357/ad7d90

    work page doi:10.3847/1538-4357/ad7d90 2024

  55. [55]

    D., Nissanke S

    Mukherjee, S., Wandelt, B. D., Nissanke, S. M., & Silvestri, A. 2021, Phys. Rev. D, 103, 043520, doi: 10.1103/PhysRevD.103.043520

    work page doi:10.1103/physrevd.103.043520 2021

  56. [56]

    D., & Silk, J

    Mukherjee, S., Wandelt, B. D., & Silk, J. 2020, Mon. Not. Roy. Astron. Soc., 494, 1956, doi: 10.1093/mnras/staa827

    work page doi:10.1093/mnras/staa827 2020

  57. [57]

    2016, PhRvL, 116, 121302, doi: 10.1103/PhysRevLett.116.121302

    Namikawa, T., Nishizawa, A., & Taruya, A. 2016, PhRvL, 116, 121302, doi: 10.1103/PhysRevLett.116.121302

    work page doi:10.1103/physrevlett.116.121302 2016

  58. [58]

    L., Neilsen, D., et al

    Palenzuela, C., Liebling, S. L., Neilsen, D., et al. 2015, PhRvD, 92, 044045, doi: 10.1103/PhysRevD.92.044045

    work page doi:10.1103/physrevd.92.044045 2015

  59. [59]

    V., Mehrtens, N., et al

    Papovich, C., Shipley, H. V., Mehrtens, N., et al. 2016, ApJS, 224, 28, doi: 10.3847/0067-0049/224/2/28

    work page doi:10.3847/0067-0049/224/2/28 2016

  60. [60]

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

    Poulin, V., Smith, T. L., Karwal, T., & Kamionkowski, M. 2019, PhRvL, 122, 221301, doi: 10.1103/PhysRevLett.122.221301

    work page doi:10.1103/physrevlett.122.221301 2019

  61. [61]

    arXiv.org , author =

    Price-Whelan, A. M., Sip˝ ocz, B. M., G¨ unther, H. M., et al. 2018, The Astronomical Journal, 156, 123, doi: 10.3847/1538-3881/aabc4f

    work page doi:10.3847/1538-3881/aabc4f 2018

  62. [62]

    W., Adams, M

    Ramsey, L. W., Adams, M. T., Barnes, T. G., et al. 1998, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 3352, Advanced Technology Optical/IR Telescopes VI, ed. L. M. Stepp, 34–42, doi: 10.1117/12.319287

    work page doi:10.1117/12.319287 1998

  63. [63]

    G., et al., 2022, @doi [The Astrophysical Journal Letters] 10.3847/2041-8213/ac5c5b , 934, L7

    Riess, A. G., et al. 2022, ApJL, 934, L7, doi: 10.3847/2041-8213/ac5c5b

    work page doi:10.3847/2041-8213/ac5c5b 2022

  64. [64]

    G., Li, S., Anand, G

    Riess, A. G., Li, S., Anand, G. S., et al. 2025, ApJL, 992, L34, doi: 10.3847/2041-8213/ae0ad6

    work page doi:10.3847/2041-8213/ae0ad6 2025

  65. [65]

    J., Gronwall, C., Lipovetsky, V

    Salzer, J. J., Gronwall, C., Lipovetsky, V. A., et al. 2000, AJ, 120, 80, doi: 10.1086/301418

    work page doi:10.1086/301418 2000

  66. [66]

    1976, Astrophys

    Schechter, P. 1976, Astrophys. J., 203, 297, doi: 10.1086/154079

    work page doi:10.1086/154079 1976

  67. [67]

    F., Finkbeiner D

    Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103, doi: 10.1088/0004-637X/737/2/103

    work page internal anchor Pith review doi:10.1088/0004-637x/737/2/103 2011

  68. [68]

    Maps of Dust IR Emission for Use in Estimation of Reddening and CMBR Foregrounds

    Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525, doi: 10.1086/305772

    work page internal anchor Pith review doi:10.1086/305772 1998

  69. [69]

    , year = 1968, month = feb, volume =

    Schmidt, M. 1968, ApJ, 151, 393, doi: 10.1086/149446

    work page doi:10.1086/149446 1968

  70. [70]

    Schutz, B. F. 1986, Nature, 323, 310, doi: 10.1038/323310a0

    work page doi:10.1038/323310a0 1986

  71. [71]

    Schutz, B. F. 2011, Class. Quant. Grav., 28, 125023, doi: 10.1088/0264-9381/28/12/125023

    work page doi:10.1088/0264-9381/28/12/125023 2011

  72. [72]

    2006, The Cosmic Evolution Survey (COSMOS) – Overview, doi: 10.1086/516585

    Scoville, N., et al. 2007, ApJS, 172, 1, doi: 10.1086/516585

    work page doi:10.1086/516585 2007

  73. [73]

    R., Gair J

    Taylor, S. R., & Gair, J. R. 2012, PhRvD, 86, 023502, doi: 10.1103/PhysRevD.86.023502

    work page doi:10.1103/physrevd.86.023502 2012

  74. [74]

    Verde, L., Treu, T., & Riess, A. G. 2019, Nature Astron., 3, 891, doi: 10.1038/s41550-019-0902-0

    work page internal anchor Pith review doi:10.1038/s41550-019-0902-0 2019

  75. [75]

    Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, St´ efan J

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261–272, doi: 10.1038/s41592-019-0686-2

    work page doi:10.1038/s41592-019-0686-2 2020

  76. [76]

    2019, PhRvD, 100, 043012, doi: 10.1103/PhysRevD.100.043012

    Wysocki, D., Lange, J., & O’Shaughnessy, R. 2019, PhRvD, 100, 043012, doi: 10.1103/PhysRevD.100.043012

    work page doi:10.1103/physrevd.100.043012 2019

  77. [77]

    Relative Binning and Fast Likelihood Evaluation for Gravitational Wave Parameter Estimation

    Zackay, B., Dai, L., & Venumadhav, T. 2018, https://arxiv.org/abs/1806.08792

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  78. [78]

    R., Debski, M

    Zeimann, G. R., Debski, M. H., Schneider, D. P., et al. 2024, ApJ, 966, 14, doi: 10.3847/1538-4357/ad35b8

    work page doi:10.3847/1538-4357/ad35b8 2024

  79. [79]

    2025, https://arxiv.org/abs/2508.00291

    Zhang, H., Kokubo, M., MacBride, S., et al. 2025, https://arxiv.org/abs/2508.00291

    work page arXiv 2025