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arxiv: 2604.07438 · v1 · submitted 2026-04-08 · 🌌 astro-ph.CO · astro-ph.GA

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LSST Strong Lensing Systems Dark Matter Sensitivity Analysis with Neural Ratio Estimators

Andreas Filipp, Daniel Gilman, Laurence Perreault-Levasseur, LSST Dark Energy Science Collaboration, Yashar Hezaveh

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Pith reviewed 2026-05-10 17:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords strong gravitational lensingdark matter substructureLSSTneural ratio estimatorshalo mass functionline-of-sight haloscosmologysub-galactic scales
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The pith

LSST forecasts show that analyzing 2500 strong lenses can exclude 74 percent of the dark matter halo mass function prior volume at 3 sigma.

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

The paper simulates large samples of galaxy-galaxy strong lensing systems as they will appear in the LSST ten-year survey to forecast how well they can constrain dark matter properties on sub-galactic scales. Neural ratio estimators are used to infer parameters of the halo mass function from images that include both subhalos inside the main lens galaxy and halos along the line of sight, with masses extending down to 10 million solar masses. The constraining power grows strongly with sample size, moving from broad posteriors with a few hundred lenses to the ability to rule out large fractions of the prior space with thousands of systems. The sensitivity receives measurable contributions from both the high-mass and low-mass ends of the halo distribution as well as from line-of-sight structures, especially at higher redshifts.

Core claim

Simulations of LSST-quality strong lensing data demonstrate that combining 2500 lenses allows exclusion of approximately 74 percent of the considered prior volume at the 3 sigma level and 36 percent at the 5 sigma level for halo mass function parameters. This level of constraint is sufficient to distinguish Lambda-CDM from many non-standard dark matter scenarios. The signal arises from the full halo population, since removing halos below 10 to the 7.5 solar masses shifts the posteriors, and line-of-sight halos contribute an increasing fraction of the information at higher redshifts.

What carries the argument

Neural ratio estimators trained on simulated strong lensing images that incorporate dark matter subhalos and line-of-sight halos down to 10^7 solar masses.

Load-bearing premise

The entire forecast assumes that the simulations perfectly reproduce the actual data-generating process, including all noise and modeling details.

What would settle it

Measuring posteriors from real LSST data on 2500 strong lenses that exclude far less than 74 percent of the prior volume at 3 sigma would falsify the claimed sensitivity.

Figures

Figures reproduced from arXiv: 2604.07438 by Andreas Filipp, Daniel Gilman, Laurence Perreault-Levasseur, LSST Dark Energy Science Collaboration, Yashar Hezaveh.

Figure 1
Figure 1. Figure 1: Illustration of the convergence maps to raytrace through in multi plane lensing at different redshifts, with the main deflector in the middle. deviations from the ΛCDM model in a model-agnostic way, where the parameters (A, γ) = (1, 1) correspond to ΛCDM predictions. When varying the slope γ, we normalize the amplitude of the powerlaw to have the same integrated mass in dark matter halos as for the corresp… view at source ↗
Figure 2
Figure 2. Figure 2: shows the redshift distributions from which we sample. We strictly enforce the physical condition that the source redshift (zs) must be greater than the corresponding lens redshift (zl) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fifteen example lensing images generated from simulated LSST data. The set includes quadruply imaged systems (quads), doubles, and Einstein rings. ing truncated NFW (tNFW) profiles (see, Navarro et al. 1997; Baltz et al. 2009). Given the large number of these halos, we use H = {m1, m2, ...} to denote the set of parameters for the en￾tire halo population (e.g., redshifts, positions, masses, and truncation r… view at source ↗
Figure 4
Figure 4. Figure 4: Posterior constraints on DM halo population parameters for 250, 500, 1 000, and 2 500 strong lens systems, sampled from the expected LSST redshift distribution. The contours denote 1σ, 2σ, and 3σ confidence regions inferred by the NRE. The blue star marks the CDM prediction. teriors on the slope of the dark matter HMF compa￾rable with other probes such as the Ly-α forest (e.g., Viel et al. 2005, 2013; Vill… view at source ↗
Figure 5
Figure 5. Figure 5: Posterior constraints with different minimum halo mass cuts. The contours denote the 3σ constraints from 500 lens systems. Even removing the lowest mass halos below mhalo ≤ 7.5 log10 M⊙ induces a noticeable shift relative to the full sample. Additionally, the posterior estimates seem to broaden when low-mass halos are removed. pared these to the full sample which extends to a min￾imum mass of log(mhalo,min… view at source ↗
read the original abstract

Strong gravitational lensing offers a unique probe of dark matter (DM) on sub-galactic scales, where the abundance and distribution of low-mass halos are highly sensitive to the underlying properties of DM particles. In this work, we forecast LSST's sensitivity to DM substructure in galaxy-galaxy strong lenses using simulated samples and neural ratio estimators (NREs). Our simulations include both subhalos within the main deflector and line-of-sight (LOS) halos, with halo masses down to $\sim 10^7 M_\odot$ under the expected LSST ten-year survey imaging quality. We show that the constraining power on halo mass function (HMF) parameters improves significantly with sample size. Analyses based on a few hundred lenses yield broad posteriors comparable with other probes like the Ly-$\alpha$ forest. By contrast, when combining 2500 lenses, $\approx 74\%$ and $\approx 36\%$ of the prior volume considered can be excluded at the $3\sigma$ and $5\sigma$ levels respectively, enabling statistically significant exclusions of non-$\Lambda$CDM scenarios. We further demonstrate that the sensitivity arises not only from the high-mass end of the HMF but also from low-mass halos: masking halos below $\log (m_{\rm halo}/M_\odot) \leq 7.5$ induces a measurable shift in the inferred posteriors. Finally, we find that LOS halos contribute significantly to the constraining power, with increasing importance of LOS halos at higher redshifts. While this analysis assumes perfect knowledge of the data-generating process and cannot be directly applied to data analysis, it quantifies constraints achievable with LSST alone and motivates the development of robust inference methods for real survey data.

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

1 major / 3 minor

Summary. The paper forecasts LSST's constraining power on dark matter halo mass function (HMF) parameters using simulated strong-lensing systems analyzed with neural ratio estimators (NREs). Simulations incorporate both subhalos and line-of-sight halos down to ~10^7 M_⊙ under ten-year LSST imaging quality. Key results include scaling of posterior constraints with sample size, exclusion of ~74% and ~36% of the considered prior volume at 3σ and 5σ with 2500 lenses, measurable impact from low-mass halos (via masking tests), and significant contribution from LOS halos that increases with redshift. The analysis is explicitly conditioned on perfect knowledge of the data-generating process.

Significance. This simulation-based forecast quantifies the statistical power of LSST strong lensing for sub-galactic DM probes and demonstrates the utility of NREs for handling large lens samples. The explicit scaling with sample size, the masking experiment isolating low-mass halo contributions, and the redshift-dependent LOS role provide concrete, falsifiable benchmarks that can guide method development. The paper's transparent boundary condition (perfect knowledge) allows the reported exclusion fractions to be interpreted correctly as an upper-bound forecast rather than a direct data-analysis claim.

major comments (1)
  1. [§4] §4 (results on 2500-lens sample): the 74%/36% prior-volume exclusion figures at 3σ/5σ are load-bearing for the central claim, yet the text does not state the precise definition of the prior volume (e.g., the exact ranges and priors on HMF slope/normalization) nor the exact procedure used to convert NRE posterior samples into these volume-exclusion percentages; a short appendix or equation would make the numbers directly reproducible.
minor comments (3)
  1. [Abstract] Abstract and §1: the phrase 'enabling statistically significant exclusions of non-ΛCDM scenarios' is slightly overstated given the perfect-knowledge assumption; a qualifier such as 'under idealized conditions' would align the language with the explicit caveat later in the text.
  2. [Figure 5] Figure 5 (or equivalent masking panel): the shift in posteriors when masking halos below log(m_halo/M_⊙) = 7.5 is shown, but the caption does not indicate the number of realizations or the precise HMF parameter ranges used; adding this would clarify the robustness of the low-mass contribution claim.
  3. [§3.2] §3.2 (NRE training): the architecture and training details are summarized, but the loss function, number of simulations per training batch, and convergence diagnostics are not reported; these are standard for reproducibility of ratio-estimator results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation and recommendation for minor revision. We address the single major comment below and will update the manuscript accordingly.

read point-by-point responses

  1. Referee: §4 (results on 2500-lens sample): the 74%/36% prior-volume exclusion figures at 3σ/5σ are load-bearing for the central claim, yet the text does not state the precise definition of the prior volume (e.g., the exact ranges and priors on HMF slope/normalization) nor the exact procedure used to convert NRE posterior samples into these volume-exclusion percentages; a short appendix or equation would make the numbers directly reproducible.

    Authors: We agree that the exact prior ranges on the HMF parameters and the procedure for computing the excluded prior volume fractions should be stated explicitly for reproducibility. In the revised manuscript we will add a short appendix (or dedicated subsection in §4) that specifies the prior ranges and functional forms for the HMF slope and normalization, together with the precise equation used to convert the NRE posterior samples into the reported 3σ and 5σ prior-volume exclusion percentages. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forecast is self-contained simulation result

full rationale

The paper's central result is a forecast of exclusion power on HMF parameters obtained by training neural ratio estimators on large suites of forward simulations of strong lenses (including subhalos and LOS halos) and then evaluating posterior volume exclusion against external priors. No equation or step reduces the reported 74%/36% exclusion fractions (or the sensitivity to low-mass halos or LOS contributions) to a fitted parameter defined by the same data; the analysis is explicitly conditioned on perfect knowledge of the data-generating process and does not claim applicability to real observations. No self-citation is load-bearing for the forecast numbers, and no ansatz, uniqueness theorem, or renaming of a known result is invoked to force the outcome.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The forecast rests on simulated populations of subhalos and LOS halos whose abundance and mass function are drawn from priors; the neural ratio estimator training assumes the forward model exactly matches the data-generating process.

free parameters (2)
  • HMF slope and normalization parameters
    These are the target parameters being constrained; their prior ranges are scanned in the simulation.
  • Lens and source redshift distributions
    Chosen to match expected LSST samples but not derived from first principles.
axioms (2)
  • domain assumption The data-generating process (lens modeling, halo populations, imaging quality) is known perfectly
    Explicitly stated in the abstract as a limitation.
  • domain assumption Neural ratio estimators can accurately recover the likelihood ratio for the chosen summary statistics
    Underlying assumption of the inference method used.

pith-pipeline@v0.9.0 · 5649 in / 1512 out tokens · 36222 ms · 2026-05-10T17:29:53.633891+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages · 1 internal anchor

  1. [1]

    A., Marshall, P., & Oguri, M

    Baltz, E. A., Marshall, P., & Oguri, M. 2009, JCAP, 2009, 015, doi: 10.1088/1475-7516/2009/01/015

    work page doi:10.1088/1475-7516/2009/01/015 2009

  2. [2]

    , keywords =

    Bode, P., Ostriker, J. P., & Turok, N. 2001, ApJ, 556, 93, doi: 10.1086/321541

    work page doi:10.1086/321541 2001

  3. [3]

    2018, Constraining Effective Field Theories with Machine Learning

    Brehmer, J., Cranmer, K., Louppe, G., & Pavez, J. 2018, Constraining Effective Field Theories with Machine Learning. https://arxiv.org/abs/1805.00013

    work page arXiv 2018

  4. [4]

    Mining gold from implicit models to improve likelihood-free inference.Proceedings of the National Academy of Sciences, 117(10):5242–5249, 2020

    Brehmer, J., Louppe, G., Pavez, J., & Cranmer, K. 2020, Proceedings of the National Academy of Sciences, 117, 5242, doi: 10.1073/pnas.1915980117

    work page doi:10.1073/pnas.1915980117 2020

  5. [5]

    2019, ApJ, 886, 49, doi: 10.3847/1538-4357/ab4c41 Campeau-Poirier, `E., Perreault-Levasseur, L., Coogan, A., & Hezaveh, Y

    Brehmer, J., Mishra-Sharma, S., Hermans, J., Louppe, G., & Cranmer, K. 2019, ApJ, 886, 49, doi: 10.3847/1538-4357/ab4c41 Campeau-Poirier, `E., Perreault-Levasseur, L., Coogan, A., & Hezaveh, Y. 2023, in Machine Learning for Astrophysics, 6, doi: 10.48550/arXiv.2309.16063 Col´ ın, P., Avila-Reese, V., & Valenzuela, O. 2000, ApJ, 542, 622, doi: 10.1086/317057

    work page doi:10.3847/1538-4357/ab4c41 2019

  6. [6]

    Collett, T. E. 2015, ApJ, 811, 20, doi: 10.1088/0004-637X/811/1/20

    work page doi:10.1088/0004-637x/811/1/20 2015

  7. [7]

    A., Karchev, K., et al

    Coogan, A., Montel, N. A., Karchev, K., et al. 2022, One never walks alone: the effect of the perturber population on subhalo measurements in strong gravitational lenses. https://arxiv.org/abs/2209.09918

    work page arXiv 2022

  8. [8]

    Cranmer, J

    Cranmer, K., Pavez, J., & Louppe, G. 2015, arXiv e-prints, arXiv:1506.02169, doi: 10.48550/arXiv.1506.02169

    work page doi:10.48550/arxiv.1506.02169 2015

  9. [9]

    and Kuhlen, M

    Diemand, J., Kuhlen, M., & Madau, P. 2007, ApJ, 667, 859, doi: 10.1086/520573

    work page doi:10.1086/520573 2007

  10. [10]

    2025a, arXiv e-prints, arXiv:2511.13669, doi: 10.48550/arXiv.2511.13669

    Erickson, S., Millon, M., Venkatraman, P., et al. 2025a, arXiv e-prints, arXiv:2511.13669, doi: 10.48550/arXiv.2511.13669

    work page doi:10.48550/arxiv.2511.13669

  11. [11]

    2025b, AJ, 170, 44, doi: 10.3847/1538-3881/add99f

    Erickson, S., Wagner-Carena, S., Marshall, P., et al. 2025b, AJ, 170, 44, doi: 10.3847/1538-3881/add99f

    work page doi:10.3847/1538-3881/add99f

  12. [12]

    Ferreira, E. G. M. 2021, A&A Rv, 29, 7, doi: 10.1007/s00159-021-00135-6

    work page doi:10.1007/s00159-021-00135-6 2021

  13. [13]

    2025, ApJ, 989, 226, doi: 10.3847/1538-4357/adee20

    Filipp, A., Hezaveh, Y., & Perreault-Levasseur, L. 2025, ApJ, 989, 226, doi: 10.3847/1538-4357/adee20

    work page doi:10.3847/1538-4357/adee20 2025

  14. [14]

    2021, JCAP, 2021, 024, doi: 10.1088/1475-7516/2021/08/024

    Fleury, P., Larena, J., & Uzan, J.-P. 2021, JCAP, 2021, 024, doi: 10.1088/1475-7516/2021/08/024

    work page doi:10.1088/1475-7516/2021/08/024 2021

  15. [15]

    2020, MNRAS, 491, 6077, doi: 10.1093/mnras/stz3480 13

    Gilman, D., Birrer, S., Nierenberg, A., et al. 2020, MNRAS, 491, 6077, doi: 10.1093/mnras/stz3480 13

    work page doi:10.1093/mnras/stz3480 2020

  16. [16]

    Deep residual learning for image recognition

    He, K., Zhang, X., Ren, S., & Sun, J. 2016, in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1, doi: 10.1109/CVPR.2016.90

    work page doi:10.1109/cvpr.2016.90 2016

  17. [17]

    D., Dalal, N., Marrone, D

    Hezaveh, Y. D., Dalal, N., Marrone, D. P., et al. 2016, ApJ, 823, 37, doi: 10.3847/0004-637X/823/1/37

    work page doi:10.3847/0004-637x/823/1/37 2016

  18. [18]

    Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results

    Hinshaw, G., Larson, D., Komatsu, E., et al. 2013, ApJS, 208, 19, doi: 10.1088/0067-0049/208/2/19

    work page Pith review doi:10.1088/0067-0049/208/2/19 2013

  19. [19]

    2018, PhRvD, 97, 123002, doi: 10.1103/PhysRevD.97.123002

    Hiroshima, N., Ando, S., & Ishiyama, T. 2018, PhRvD, 97, 123002, doi: 10.1103/PhysRevD.97.123002

    work page doi:10.1103/physrevd.97.123002 2018

  20. [20]

    B., Nightingale, J

    Hogg, N. B., Nightingale, J. W., He, Q., et al. 2025, arXiv e-prints, arXiv:2503.08785, doi: 10.48550/arXiv.2503.08785

    work page doi:10.48550/arxiv.2503.08785 2025

  21. [21]

    Physical Review Letters85, 1158–1161 (2000) https://doi.org/ 10.1103/PhysRevLett.85.1158

    Hu, W., Barkana, R., & Gruzinov, A. 2000, PhRvL, 85, 1158, doi: 10.1103/PhysRevLett.85.1158 Ivezi´ c,ˇZ., Kahn, S. M., & Tyson, J. A. e. a. 2019a, ApJ, 873, 111, doi: 10.3847/1538-4357/ab042c Ivezi´ c,ˇZ., Kahn, S. M., Tyson, J. A., et al. 2019b, ApJ, 873, 111, doi: 10.3847/1538-4357/ab042c

    work page doi:10.1103/physrevlett.85.1158 2000

  22. [22]

    2024, arXiv e-prints, arXiv:2407.17292, doi: 10.48550/arXiv.2407.17292

    Jarugula, S., Nord, B., Gandrakota, A., & ´Ciprijanovi´ c, A. 2024, arXiv e-prints, arXiv:2407.17292, doi: 10.48550/arXiv.2407.17292

    work page doi:10.48550/arxiv.2407.17292 2024

  23. [23]

    Adam: A Method for Stochastic Optimization

    Kingma, D. P., & Ba, J. 2014, arXiv e-prints, arXiv:1412.6980, doi: 10.48550/arXiv.1412.6980

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980 2014

  24. [24]

    2007, ApJ, 671, 1135, doi: 10.1086/522878

    Kuhlen, M., Diemand, J., & Madau, P. 2007, ApJ, 671, 1135, doi: 10.1086/522878

    work page doi:10.1086/522878 2007

  25. [25]

    2022, A&A, 668, A166, doi: 10.1051/0004-6361/202244978 LSST Science Collaboration, Abell, P

    Loudas, N., Pavlidou, V., Casadio, C., & Tassis, K. 2022, A&A, 668, A166, doi: 10.1051/0004-6361/202244978 LSST Science Collaboration, Abell, P. A., Allison, J., & et al. 2009, arXiv e-prints, arXiv:0912.0201. https://arxiv.org/abs/0912.0201

    work page doi:10.1051/0004-6361/202244978 2022

  26. [26]

    , year = 1997, month = dec, volume = 490, pages =

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493, doi: 10.1086/304888 Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910

    work page doi:10.1086/304888 1997

  27. [27]

    2025, JCAP, 2025, 053, doi: 10.1088/1475-7516/2025/05/053

    Poh, J., Samudre, A., ´Ciprijanovi´ c, A., et al. 2025, JCAP, 2025, 053, doi: 10.1088/1475-7516/2025/05/053

    work page doi:10.1088/1475-7516/2025/05/053 2025

  28. [28]

    K., & Poulin, V

    Rogers, K. K., & Poulin, V. 2025, Physical Review Research, 7, L012018, doi: 10.1103/PhysRevResearch.7.L012018

    work page doi:10.1103/physrevresearch.7.l012018 2025

  29. [29]

    2014, ApJL, 793, L10, doi: 10.1088/2041-8205/793/1/L10 S´ ersic, J

    Serjeant, S. 2014, ApJL, 793, L10, doi: 10.1088/2041-8205/793/1/L10 S´ ersic, J. L. 1963, Boletin de la Asociacion Argentina de Astronomia La Plata Argentina, 6, 41

    work page doi:10.1088/2041-8205/793/1/l10 2014

  30. [30]

    G., Staveley-Smith, L., de Blok, W

    Sheth, R. K., Mo, H. J., & Tormen, G. 2001, MNRAS, 323, 1, doi: 10.1046/j.1365-8711.2001.04006.x

    work page doi:10.1046/j.1365-8711.2001.04006.x 2001

  31. [31]

    J., Schawinski, K., Slosar, A., et al

    Springel, V., Wang, J., Vogelsberger, M., et al. 2008, MNRAS, 391, 1685, doi: 10.1111/j.1365-2966.2008.14066.x

    work page doi:10.1111/j.1365-2966.2008.14066.x 2008

  32. [32]

    2024, arXiv e-prints, arXiv:2406.15542, doi: 10.48550/arXiv.2406.15542

    Stone, C., Adam, A., Coogan, A., et al. 2024, arXiv e-prints, arXiv:2406.15542, doi: 10.48550/arXiv.2406.15542

    work page doi:10.48550/arxiv.2406.15542 2024

  33. [33]

    2018, arXiv e-prints, arXiv:1808.00973, doi: 10.48550/arXiv.1808.00973

    Stoye, M., Brehmer, J., Louppe, G., Pavez, J., & Cranmer, K. 2018, arXiv e-prints, arXiv:1808.00973, doi: 10.48550/arXiv.1808.00973

    work page doi:10.48550/arxiv.1808.00973 2018

  34. [34]

    Tessore, N., & Metcalf, R. B. 2015, A&A, 580, A79, doi: 10.1051/0004-6361/201526773

    work page doi:10.1051/0004-6361/201526773 2015

  35. [35]

    2025, arXiv e-prints, arXiv:2509.13318, doi: 10.48550/arXiv.2509.13318

    Freese, K. 2025, arXiv e-prints, arXiv:2509.13318, doi: 10.48550/arXiv.2509.13318

    work page doi:10.48550/arxiv.2509.13318 2025

  36. [36]

    2011, MNRAS, 410, 166, doi: 10.1111/j.1365-2966.2010.17432.x

    Gavazzi, R. 2010, MNRAS, 408, 1969, doi: 10.1111/j.1365-2966.2010.16865.x

    work page doi:10.1111/j.1365-2966.2010.16865.x 2010

  37. [37]

    2025, arXiv e-prints, arXiv:2510.20778, doi: 10.48550/arXiv.2510.20778

    Venkatraman, P., Erickson, S., Marshall, P., et al. 2025, arXiv e-prints, arXiv:2510.20778, doi: 10.48550/arXiv.2510.20778

    work page doi:10.48550/arxiv.2510.20778 2025

  38. [38]

    D., Bolton, J

    Viel, M., Becker, G. D., Bolton, J. S., & Haehnelt, M. G. 2013, PhRvD, 88, 043502, doi: 10.1103/PhysRevD.88.043502

    work page doi:10.1103/physrevd.88.043502 2013

  39. [39]

    http://www.w3.org/1998/Math/MathML

    Viel, M., Lesgourgues, J., Haehnelt, M. G., Matarrese, S., & Riotto, A. 2005, PhRvD, 71, 063534, doi: 10.1103/PhysRevD.71.063534

    work page doi:10.1103/physrevd.71.063534 2005

  40. [40]

    http://www.w3.org/1998/Math/MathML

    Villasenor, B., Robertson, B., Madau, P., & Schneider, E. 2023, PhRvD, 108, 023502, doi: 10.1103/PhysRevD.108.023502

    work page doi:10.1103/physrevd.108.023502 2023

  41. [41]

    2023, ApJ, 942, 75, doi: 10.3847/1538-4357/aca525

    Wagner-Carena, S., Aalbers, J., Birrer, S., et al. 2023, ApJ, 942, 75, doi: 10.3847/1538-4357/aca525

    work page doi:10.3847/1538-4357/aca525 2023

  42. [42]

    2024, arXiv e-prints, arXiv:2404.14487, doi: 10.48550/arXiv.2404.14487

    Wagner-Carena, S., Lee, J., Pennington, J., et al. 2024, arXiv e-prints, arXiv:2404.14487, doi: 10.48550/arXiv.2404.14487

    work page doi:10.48550/arxiv.2404.14487 2024

  43. [43]

    C ¸ ., & Dvorkin, C

    Zhang, G., S ¸eng¨ ul, A. C ¸ ., & Dvorkin, C. 2024, MNRAS, 527, 4183, doi: 10.1093/mnras/stad3521

    work page doi:10.1093/mnras/stad3521 2024