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arxiv: 2512.25040 · v2 · pith:5GOOW2XPnew · submitted 2025-12-31 · 🌌 astro-ph.CO

Towards precision cosmology with Voids x CMB correlations (I): Roman-Agora mock catalogs and pipeline validation

Pith reviewed 2026-05-22 11:48 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords analog matchingmock galaxy catalogsvoid statisticsgalaxy-halo connectionRoman Space TelescopeCMB cross-correlationslarge-scale structure
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The pith

Analog matching on halo mass reproduces Roman emission-line galaxy statistics while voids supply independent constraints on galaxy-halo connections

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

The paper builds multi-purpose mock galaxy catalogs for the Nancy Grace Roman Space Telescope by translating properties from a reference catalog into the Agora simulation through analog matching. This technique performs a nearest-neighbor search in a multi-dimensional space that can include halo mass, environmental measures, and galaxy attributes, allowing tests of how different galaxy-halo prescriptions affect large-scale structure observables and CMB cross-correlations. Matching based on halo mass alone or combined with galaxy-type indicators reproduces the target emission-line galaxy statistics. Reproducing two-dimensional galaxy clustering does not automatically produce consistent void properties, showing that voids offer independent and sensitive information on galaxy-halo relations beyond what the matter power spectrum provides. The method is general and yields versatile catalogs for LSS x CMB analyses.

Core claim

Analog matching based on halo mass alone, or halo mass and galaxy-type indicators, successfully reproduces the expected Roman emission-line galaxy statistics, while reproducing two-dimensional galaxy clustering does not guarantee consistent void properties, demonstrating that voids provide independent constraints on galaxy-halo connections.

What carries the argument

Analog matching: nearest-neighbor search in a multi-dimensional parameter space of halo mass, environment, and galaxy attributes to assign halo counterparts from a reference catalog to galaxies in a target simulation.

If this is right

  • Voids can be used to validate mock catalogs for cosmological analyses involving cross-correlations with the CMB.
  • Different galaxy-halo models that agree on clustering statistics can be distinguished using void properties.
  • The mock catalogs serve as a benchmark for assessing the impact of mock accuracy on cosmological observables from LSS x CMB studies.
  • The general analog matching approach can be applied to any combination of simulation and reference catalog.

Where Pith is reading between the lines

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

  • Future surveys could incorporate void measurements to break degeneracies in galaxy formation models that persist after clustering matches.
  • Extending the matching parameter space with additional environmental measures might further improve consistency in higher-order void statistics.
  • The results suggest applying void-finding algorithms consistently between mocks and observations to enable fair comparisons in precision cosmology.

Load-bearing premise

Nearest-neighbor matching in the chosen multi-dimensional parameter space preserves the higher-order statistics needed for void identification and void-CMB cross-correlations.

What would settle it

A direct comparison revealing significant differences in void size distributions or void-CMB cross-correlation amplitudes between the analog-matched mocks and the reference catalog when using only halo mass matching.

Figures

Figures reproduced from arXiv: 2512.25040 by Alice Pisani, Andr\'as Kov\'acs, Carlos Hern\'andez Monteagudo, Mar P\'erez Sar.

Figure 1
Figure 1. Figure 1: Flowchart illustrating the datasets and methodology employed in this paper. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Slice at z = 1.012 with thickness ∆z = 0.01, illustrating 3D and 2D voids identified with the void finder with smoothing scales of 5 and 10 Mpc h −1 . To maintain clarity, only voids centered at this exact redshift are plotted; otherwise, including the full slice width would result in 3D voids covering the map. Specifically, we identify 525 3D voids (restricted to this redshift), compared to 470 2D voids a… view at source ↗
Figure 3
Figure 3. Figure 3: One-point statistic distributions for the generated void catalogs. The rows correspond to the void redshift (top), void size [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Two-point statistics including the galaxy power spectrum (top panel) and the galaxy-void cross-correlation function. For [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
read the original abstract

We construct and validate a set of multi-purpose mock galaxy catalogs designed to capture, to different degrees of accuracy, the main characteristics of the Nancy Grace Roman Space Telescope survey. These catalogs provide a foundation for void statistics and various CMB cross-correlation analyses. Our approach differs from traditional halo occupation or abundance matching methods by directly translating a reference mock catalog -- containing basic properties of the host halos -- into a new simulation (in our case Agora). This technique, which we call analog matching, assigns a halo counterpart in the new simulation to each reference galaxy through a nearest-neighbor search in a multi-dimensional parameter space. This space can include halo mass, environmental measures and other galaxy-specific attributes. By varying the composition of this parameter vector, we can generate catalogs of differing complexity and test how galaxy-halo prescriptions influence LSS statistics and CMB-related observables. We find that analog matching based on halo mass alone, or halo mass and galaxy-type indicators, successfully reproduces the expected Roman emission-line galaxy statistics. We also show that reproducing two-dimensional galaxy clustering does not guarantee consistent void properties. Our results highlight the importance of matching void statistics for improved mock accuracy, and demonstrate that measuring voids provides independent and sensitive constraints on galaxy-halo connections beyond the matter power spectrum. An important by-product of our setup is that it is fully general and can be applied to any combination of simulation and reference catalog, provided that the desired parameter space for both is specified. The resulting Roman-Agora mock catalogs offer a versatile resource for LSS x CMB studies and a benchmark for assessing the impact of mock accuracy on cosmological observables.

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 introduces an 'analog matching' technique to generate mock catalogs for the Nancy Grace Roman Space Telescope by performing nearest-neighbor assignment of halos from a reference catalog to the Agora simulation in a multi-dimensional parameter space (halo mass, environment, galaxy attributes). It validates that mass-only or mass-plus-type matching reproduces Roman ELG number densities and basic statistics, while showing that successful reproduction of two-dimensional galaxy clustering does not guarantee matching void properties, thereby arguing that void statistics supply independent constraints on galaxy-halo connections for LSS x CMB analyses.

Significance. If the results hold, the work supplies a flexible, general-purpose framework for mock generation that can be applied to arbitrary simulation-reference pairs and serves as a benchmark for quantifying how galaxy-halo modeling choices propagate into void-CMB cross-correlations. The explicit demonstration that 2D clustering reproduction is insufficient for void consistency is a useful contribution, highlighting the sensitivity of higher-order LSS observables.

major comments (2)
  1. [Results section on void properties] The central claim that 'reproducing two-dimensional galaxy clustering does not guarantee consistent void properties' (abstract and results section) depends on the untested assumption that nearest-neighbor selection in the chosen parameter vector preserves the higher-order correlations (local density, tidal field) required by the void-finding algorithm. If the environment coordinate is only a coarse proxy, the matched catalog can match the 2-point function while systematically shifting void sizes, shapes, and CMB cross-correlations, weakening the evidence for independent constraints.
  2. [§3] §3 (method): the analog-matching procedure is described without quantitative validation that the selected parameter space reproduces the exact inputs to the void finder (e.g., density or tidal-field distributions); a direct comparison of these fields between reference and matched catalogs is needed to support the claim that voids add independent information.
minor comments (2)
  1. [Abstract] The abstract states that mass-only matching 'successfully reproduces the expected Roman emission-line galaxy statistics' but does not specify which statistics (number density, luminosity function, or color distributions) or the quantitative tolerance used.
  2. [Results figures] Figures comparing void size or shape distributions would benefit from explicit error bars or statistical tests (e.g., KS p-values) to quantify the reported differences.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful report. The comments identify valuable opportunities to strengthen the validation of our analog-matching approach and its implications for void statistics. We address each major comment below and commit to revisions that directly respond to the concerns raised.

read point-by-point responses
  1. Referee: [Results section on void properties] The central claim that 'reproducing two-dimensional galaxy clustering does not guarantee consistent void properties' (abstract and results section) depends on the untested assumption that nearest-neighbor selection in the chosen parameter vector preserves the higher-order correlations (local density, tidal field) required by the void-finding algorithm. If the environment coordinate is only a coarse proxy, the matched catalog can match the 2-point function while systematically shifting void sizes, shapes, and CMB cross-correlations, weakening the evidence for independent constraints.

    Authors: We agree that the environment measure functions as a proxy and that explicit validation of higher-order fields would reinforce the interpretation. Our results already demonstrate that catalogs matched on halo mass plus environment reproduce two-point clustering yet produce statistically distinct void populations; this discrepancy itself indicates that the chosen parameter vector does not fully preserve the correlations required by the void finder. To address the concern directly, the revised manuscript will include quantitative comparisons of the local density and tidal-field distributions (PDFs and Kolmogorov-Smirnov tests) between the reference and matched catalogs, together with an assessment of how residual differences propagate into void sizes and CMB cross-correlations. revision: yes

  2. Referee: [§3] §3 (method): the analog-matching procedure is described without quantitative validation that the selected parameter space reproduces the exact inputs to the void finder (e.g., density or tidal-field distributions); a direct comparison of these fields between reference and matched catalogs is needed to support the claim that voids add independent information.

    Authors: We acknowledge that §3 currently emphasizes the matching algorithm and its validation for number densities and two-point statistics without explicit field-level comparisons. In the revised version we will expand §3 to present direct quantitative comparisons of the density and tidal-field distributions (including cumulative distribution functions and summary statistics) between the reference catalog and the analog-matched realizations. These additions will provide the requested support for the claim that void statistics supply independent constraints on galaxy-halo connections. revision: yes

Circularity Check

0 steps flagged

No circularity: validation relies on direct statistical comparisons between matched catalogs and reference expectations

full rationale

The paper's core procedure is analog matching via nearest-neighbor search in a user-specified multi-dimensional parameter space (halo mass, environment, galaxy attributes) applied to a reference catalog to produce Roman-like mocks in the Agora simulation. All reported results consist of explicit comparisons: number densities, 2D clustering, and void properties are measured on the output catalogs and contrasted against the input reference or against each other when the matching vector is varied. No quantity is defined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing premise reduces to a self-citation or prior ansatz by the same authors. The demonstration that void statistics differ even when 2D clustering matches is an empirical outcome of those controlled comparisons, not a tautology. The work is therefore self-contained against its own internal benchmarks and external reference catalogs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions in cosmological simulations and galaxy-halo modeling; no new free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption The reference mock catalog provides an accurate enough representation of galaxy properties for the purpose of matching.
    Invoked when translating the reference catalog into Agora; without this, the matched catalog inherits biases.
  • domain assumption Nearest-neighbor matching in the chosen parameter space preserves the statistics relevant for voids and CMB cross-correlations.
    Core to the validation claims in the abstract.

pith-pipeline@v0.9.0 · 5840 in / 1533 out tokens · 33359 ms · 2026-05-22T11:48:41.750472+00:00 · methodology

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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. Towards precision cosmology with Void x CMB correlations (II): Impact of mock catalogs on the Void x CMB lensing signal

    astro-ph.CO 2026-05 conditional novelty 5.0

    Void x CMB lensing from Roman mocks is robust to catalog construction choices and forecasts S/N of 13-31 sigma with Planck, SO, and CMB-S4-like data for 2D and 3D voids.

Reference graph

Works this paper leans on

174 extracted references · 174 canonical work pages · cited by 1 Pith paper · 10 internal anchors

  1. [2]

    Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2023, Phys. Rev. D, 107, 023531, doi:10.1103/PhysRevD.107.023531

  2. [3]

    Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

    Abdalla, E., Abellán, G. F., Aboubrahim, A., et al. 2022, Journal of High Energy Astrophysics, 34, 49, doi:10.1016/j.jheap.2022.04.002

  3. [4]

    Vagnozzi, L

    Achitouv, I. 2019, Phys. Rev. D, 100, 123513, doi:10.1103/PhysRevD.100. 123513

  4. [5]

    2021, MNRAS, 504, 4667, doi:10

    Alam, S., de Mattia, A., Tamone, A., et al. 2021, MNRAS, 504, 4667, doi:10. 1093/mnras/stab1150

  5. [6]

    1979, Nature, 281, 358, doi:10.1038/281358a0

    Alcock, C., & Paczynski, B. 1979, Nature, 281, 358, doi:10.1038/281358a0

  6. [7]

    G., Rodriguez, F., Ruiz, A

    Alfaro, I. G., Rodriguez, F., Ruiz, A. N., Luparello, H. E., & Lambas, D. G. 2022, A&A, 665, A44, doi:10.1051/0004-6361/202243542

  7. [8]

    2019, MNRAS, 484, 4127, doi:10.1093/mnras/stz093

    Alonso, D., Sanchez, J., Slosar, A., & LSST Dark Energy Science Collaboration. 2019, MNRAS, 484, 4127, doi:10.1093/mnras/stz093

  8. [10]

    Tracing the high-z cosmic web with Quaia: catalogues of voids and clusters in the quasar distribution

    Arsenov, N., Kovács, A., Pérez Sar, M., et al. 2025, arXiv e-prints, arXiv:2509.17696, doi:10.48550/arXiv.2509.17696

  9. [11]

    2022, MNRAS, 513, 186, doi:10.1093/mnras/stac828 Balaguera-Antolínez, A., Montero-Dorta, A

    Aubert, M., Cousinou, M.-C., Escoffier, S., et al. 2022, MNRAS, 513, 186, doi:10.1093/mnras/stac828 Balaguera-Antolínez, A., Montero-Dorta, A. D., & Favole, G. 2024, A&A, 685, A61, doi:10.1051/0004-6361/202348694

  10. [13]

    M., Bond, J

    Bardeen, J. M., Bond, J. R., Kaiser, N., & Szalay, A. S. 1986, ApJ, 304, 15, doi:10.1086/164143

  11. [14]

    Basu, K., Hernández-Monteagudo, C., & Sunyaev, R. A. 2004, A&A, 416, 447, doi:10.1051/0004-6361:20034298

  12. [15]

    E., Zhong, Y ., Li, Z., et al

    Bayer, A. E., Zhong, Y ., Li, Z., et al. 2025, J. Cosmology Astropart. Phys., 2025, 016, doi:10.1088/1475-7516/2025/05/016

  13. [16]

    H., Hearin, A

    Behroozi, P., Wechsler, R. H., Hearin, A. P., & Conroy, C. 2019, MNRAS, 488, 3143, doi:10.1093/mnras/stz1182

  14. [17]

    S., Wechsler, R

    Behroozi, P. S., Wechsler, R. H., & Wu, H.-Y . 2013, ApJ, 762, 109, doi:10. 1088/0004-637X/762/2/109

  15. [18]

    2011, Galacticus: A Semi-Analytic Model of Galaxy Formation, As- trophysics Source Code Library, record ascl:1108.004.http://ascl.net/ 1108.004

    Benson, A. 2011, Galacticus: A Semi-Analytic Model of Galaxy Formation, As- trophysics Source Code Library, record ascl:1108.004.http://ascl.net/ 1108.004

  16. [19]

    Benson, A. J. 2001, MNRAS, 325, 1039, doi:10.1046/j.1365-8711.2001. 04470.x

  17. [20]

    A., & Weinberg, D

    Berlind, A. A., & Weinberg, D. H. 2002a, ApJ, 575, 587, doi:10.1086/341469 —. 2002b, ApJ, 575, 587, doi:10.1086/341469

  18. [21]

    Biswas, R., Alizadeh, E., & Wandelt, B. D. 2010, Phys. Rev. D, 82, 023002, doi:10.1103/PhysRevD.82.023002

  19. [22]

    R., Eisenstein, D., Hogg, D

    Blanton, M. R., Eisenstein, D., Hogg, D. W., & Zehavi, I. 2006, ApJ, 645, 977, doi:10.1086/500918

  20. [23]

    2012, Journal of Low Temperature Physics, 167, 859, doi:10.1007/s10909-012-0505-y

    Bleem, L., Ade, P., Aird, K., et al. 2012, Journal of Low Temperature Physics, 167, 859, doi:10.1007/s10909-012-0505-y

  21. [24]

    Bos, E. G. P., van de Weygaert, R., Dolag, K., & Pettorino, V . 2012, MNRAS, 426, 440, doi:10.1111/j.1365-2966.2012.21478.x

  22. [25]

    Carlberg, R

    Bower, R. G., Benson, A. J., Malbon, R., et al. 2006, MNRAS, 370, 645, doi:10. 1111/j.1365-2966.2006.10519.x

  23. [26]

    2017, MNRAS, 466, 3364, doi:10

    Cai, Y .-C., Neyrinck, M., Mao, Q., et al. 2017, MNRAS, 466, 3364, doi:10. 1093/mnras/stw3299

  24. [27]

    A., & Padilla, N

    Cai, Y .-C., Taylor, A., Peacock, J. A., & Padilla, N. 2016, MNRAS, 462, 2465, doi:10.1093/mnras/stw1809

  25. [28]

    C., et al

    Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682, doi:10.1086/ 308692

  26. [29]

    2024, A&A, 689, A171, doi:10.1051/0004-6361/202348970

    Camacho-Ciurana, G., Lee, P., Arsenov, N., et al. 2024, A&A, 689, A171, doi:10.1051/0004-6361/202348970

  27. [30]

    Carbone, C., Petkova, M., & Dolag, K. 2016, J. Cosmology Astropart. Phys., 2016, 034, doi:10.1088/1475-7516/2016/07/034

  28. [31]

    E., Ade, P

    Carlstrom, J. E., Ade, P. A. R., Aird, K. A., et al. 2011, PASP, 123, 568, doi:10. 1086/659879

  29. [32]

    Castorina, E., Carbone, C., Bel, J., Sefusatti, E., & Dolag, K. 2015, J. Cosmology Astropart. Phys., 2015, 043, doi:10.1088/1475-7516/2015/07/043

  30. [33]

    2018, MNRAS, 476, 3195, doi:10

    Cautun, M., Paillas, E., Cai, Y .-C., et al. 2018, MNRAS, 476, 3195, doi:10. 1093/mnras/sty463

  31. [34]

    J., et al

    Chang, C., Omori, Y ., Baxter, E. J., et al. 2023, Phys. Rev. D, 107, 023530, doi:10.1103/PhysRevD.107.023530

  32. [35]

    M., & Wandelt, B

    Chantavat, T., Sawangwit, U., Sutter, P. M., & Wandelt, B. D. 2016, Phys. Rev. D, 93, 043523, doi:10.1103/PhysRevD.93.043523

  33. [36]

    Chen, S.-F., Lee, H., & Dvorkin, C. 2021, J. Cosmology Astropart. Phys., 2021, 030, doi:10.1088/1475-7516/2021/05/030

  34. [37]

    2019, MNRAS, 487, 48, doi:10

    Chuang, C.-H., Yepes, G., Kitaura, F.-S., et al. 2019, MNRAS, 487, 48, doi:10. 1093/mnras/stz1233

  35. [39]

    M., González Delgado, R

    Conrado, A. M., González Delgado, R. M., García-Benito, R., et al. 2024, A&A, 687, A98, doi:10.1051/0004-6361/202449414

  36. [40]

    H., & Kravtsov, A

    Conroy, C., Wechsler, R. H., & Kravtsov, A. V . 2006, ApJ, 647, 201, doi:10. 1086/503602

  37. [41]

    2023, ApJ, 953, 46, doi:10.3847/ 1538-4357/acde54 —

    Contarini, S., Pisani, A., Hamaus, N., et al. 2023, ApJ, 953, 46, doi:10.3847/ 1538-4357/acde54 —. 2024, A&A, 682, A20, doi:10.1051/0004-6361/202347572

  38. [42]

    2019a, MNRAS, 488, 3526, doi:10

    Contarini, S., Ronconi, T., Marulli, F., et al. 2019a, MNRAS, 488, 3526, doi:10. 1093/mnras/stz1989 —. 2019b, MNRAS, 488, 3526, doi:10.1093/mnras/stz1989

  39. [43]

    A., Vega-Martínez, C

    Cora, S. A., Vega-Martínez, C. A., Hough, T., et al. 2018, MNRAS, 479, 2, doi:10.1093/mnras/sty1131

  40. [44]

    M., Paz, D

    Correa, C. M., Paz, D. J., Padilla, N. D., et al. 2019, MNRAS, 485, 5761, doi:10. 1093/mnras/stz821 —. 2022a, MNRAS, 509, 1871, doi:10.1093/mnras/stab3070 —. 2022b, MNRAS, 509, 1871, doi:10.1093/mnras/stab3070

  41. [45]

    M., Paz, D

    Correa, C. M., Paz, D. J., Sánchez, A. G., et al. 2021a, MNRAS, 500, 911, doi:10.1093/mnras/staa3252 —. 2021b, MNRAS, 500, 911, doi:10.1093/mnras/staa3252

  42. [46]

    R., & Shirokov, A

    Dalal, N., White, M., Bond, J. R., & Shirokov, A. 2008, ApJ, 687, 12, doi:10. 1086/591512

  43. [47]

    D., Aguirre, P., et al

    Das, S., Sherwin, B. D., Aguirre, P., et al. 2011, Phys. Rev. Lett., 107, 021301, doi:10.1103/PhysRevLett.107.021301

  44. [48]

    2025, arXiv e-prints, arXiv:2509.08884, doi:10.48550/arXiv.2509.08884

    Degni, G., Sarpa, E., Aubert, M., et al. 2025, arXiv e-prints, arXiv:2509.08884, doi:10.48550/arXiv.2509.08884

  45. [49]

    The DESI Experiment Part I: Science,Targeting, and Survey Design

    Demirbozan, U., Nadathur, S., Ferrero, I., et al. 2024, MNRAS, 534, 2328, doi:10.1093/mnras/stae2206 DESI Collaboration, Aghamousa, A., Aguilar, J., et al. 2016, arXiv e-prints, arXiv:1611.00036, doi:10.48550/arXiv.1611.00036

  46. [50]

    2016, MNRAS, 463, 1797, doi:10

    Dolag, K., Komatsu, E., & Sunyaev, R. 2016, MNRAS, 463, 1797, doi:10. 1093/mnras/stw2035 Domínguez-Gómez, J., Pérez, I., Ruiz-Lara, T., et al. 2023, Nature, 619, 269, doi:10.1038/s41586-023-06109-1

  47. [51]

    Dancing in the dark: galactic properties trace spin swings along the cosmic web

    Dubois, Y ., Pichon, C., Welker, C., et al. 2014a, MNRAS, 444, 1453, doi:10. 1093/mnras/stu1227 —. 2014b, MNRAS, 444, 1453, doi:10.1093/mnras/stu1227 —. 2014c, MNRAS, 444, 1453, doi:10.1093/mnras/stu1227

  48. [52]

    2025, Philosophical Transactions of the Royal Society of London Series A, 383, 20240022, doi:10.1098/rsta.2024.0022

    Efstathiou, G. 2025, Philosophical Transactions of the Royal Society of London Series A, 383, 20240022, doi:10.1098/rsta.2024.0022

  49. [53]

    Faltenbacher, A., & White, S. D. M. 2010, ApJ, 708, 469, doi:10.1088/ 0004-637X/708/1/469

  50. [54]

    2019, MNRAS, 490, 3573, doi:10.1093/ mnras/stz2805

    Fang, Y ., Hamaus, N., Jain, B., et al. 2019, MNRAS, 490, 3573, doi:10.1093/ mnras/stz2805

  51. [55]

    2016, MNRAS, 461, 3421, doi:10

    Favole, G., Comparat, J., Prada, F., et al. 2016, MNRAS, 461, 3421, doi:10. 1093/mnras/stw1483 Fernández-García, E., Betancort-Rijo, J. E., Prada, F., et al. 2025, A&A, 695, A19, doi:10.1051/0004-6361/202451264

  52. [56]

    S., Paillas, E., Percival, W

    Fraser, T. S., Paillas, E., Percival, W. J., et al. 2025, J. Cosmology Astropart. Phys., 2025, 001, doi:10.1088/1475-7516/2025/06/001

  53. [57]

    Fry, J. N. 1996, ApJ, 461, L65, doi:10.1086/310006

  54. [59]

    Gao, L., Springel, V ., & White, S. D. M. 2005, MNRAS, 363, L66, doi:10. 1111/j.1745-3933.2005.00084.x

  55. [60]

    T., Ogilvie G

    Geach, J. E., Smail, I., Best, P. N., et al. 2008, MNRAS, 388, 1473, doi:10. 1111/j.1365-2966.2008.13481.x

  56. [61]

    2020, MNRAS, 498, 1852, doi:10.1093/mnras/staa2504 Article number, page 15 of 19 A&A proofs:manuscript no

    Gonzalez-Perez, V ., Cui, W., Contreras, S., et al. 2020, MNRAS, 498, 1852, doi:10.1093/mnras/staa2504 Article number, page 15 of 19 A&A proofs:manuscript no. main Górski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759, doi:10. 1086/427976

  57. [62]

    Wide-Field InfraRed Survey Telescope (WFIRST) Final Report

    Green, J., Schechter, P., Baltay, C., et al. 2012, arXiv e-prints, arXiv:1208.4012, doi:10.48550/arXiv.1208.4012

  58. [63]

    A., & Thompson, L

    Gregory, S. A., & Thompson, L. A. 1978, ApJ, 222, 784, doi:10.1086/156198

  59. [64]

    2015, MNRAS, 453, 4368, doi:10.1093/ mnras/stv1966

    Guo, H., Zheng, Z., Zehavi, I., et al. 2015, MNRAS, 453, 4368, doi:10.1093/ mnras/stv1966

  60. [65]

    Hadzhiyska, B., Bose, S., Eisenstein, D., Hernquist, L., & Spergel, D. N. 2020, MNRAS, 493, 5506, doi:10.1093/mnras/staa623

  61. [66]

    Carlberg, R

    Hahn, O., Porciani, C., Carollo, C. M., & Dekel, A. 2007, MNRAS, 375, 489, doi:10.1111/j.1365-2966.2006.11318.x

  62. [67]

    Hamaus, N., Pisani, A., Choi, J.-A., et al. 2020, J. Cosmology Astropart. Phys., 2020, 023, doi:10.1088/1475-7516/2020/12/023

  63. [68]

    M., Lavaux, G., & Wandelt, B

    Hamaus, N., Sutter, P. M., Lavaux, G., & Wandelt, B. D. 2015, J. Cosmology Astropart. Phys., 2015, 036, doi:10.1088/1475-7516/2015/11/036

  64. [69]

    M., & Wandelt, B

    Hamaus, N., Sutter, P. M., & Wandelt, B. D. 2014, Phys. Rev. Lett., 112, 251302, doi:10.1103/PhysRevLett.112.251302

  65. [70]

    2022, A&A, 658, A20, doi:10.1051/ 0004-6361/202142073

    Hamaus, N., Aubert, M., Pisani, A., et al. 2022, A&A, 658, A20, doi:10.1051/ 0004-6361/202142073

  66. [72]

    Hang, Q., Alam, S., Cai, Y .-C., & Peacock, J. A. 2021, MNRAS, 507, 510, doi:10.1093/mnras/stab2184

  67. [73]

    J., Granett, B

    Hawken, A. J., Granett, B. R., Iovino, A., et al. 2017, A&A, 607, A54, doi:10. 1051/0004-6361/201629678

  68. [74]

    2020, MNRAS, 495, 5040, doi:10

    Hearin, A., Korytov, D., Kovacs, E., et al. 2020, MNRAS, 495, 5040, doi:10. 1093/mnras/staa1495

  69. [75]

    P., Watson, D

    Hearin, A. P., Watson, D. F., Becker, M. R., et al. 2014, MNRAS, 444, 729, doi:10.1093/mnras/stu1443 Hernández-Monteagudo, C. 2019, in Highlights on Spanish Astrophysics X, ed. B. Montesinos, A. Asensio Ramos, F. Buitrago, R. Schödel, E. Villaver, S. Pérez-Hoyos, & I. Ordóñez-Etxeberria, 134–139 Hernández-Monteagudo, C., Rubiño-Martín, J. A., & Sunyaev, R...

  70. [76]

    M., Ho, S., Padmanabhan, N., Seljak, U., & Bahcall, N

    Hirata, C. M., Ho, S., Padmanabhan, N., Seljak, U., & Bahcall, N. A. 2008, Phys. Rev. D, 78, 043520, doi:10.1103/PhysRevD.78.043520

  71. [77]

    2008, Phys

    Ho, S., Hirata, C., Padmanabhan, N., Seljak, U., & Bahcall, N. 2008, Phys. Rev. D, 78, 043519, doi:10.1103/PhysRevD.78.043519 Jõeveer, M., Einasto, J., & Tago, E. 1978, MNRAS, 185, 357, doi:10.1093/ mnras/185.2.357

  72. [78]

    2025, MNRAS, 536, 1303, doi:10

    Jeffrey, N., Whiteway, L., Gatti, M., et al. 2025, MNRAS, 536, 1303, doi:10. 1093/mnras/stae2629

  73. [79]

    2013a, MNRAS, 434, 2167, doi:10.1093/ mnras/stt1169 —

    Jennings, E., Li, Y ., & Hu, W. 2013a, MNRAS, 434, 2167, doi:10.1093/ mnras/stt1169 —. 2013b, MNRAS, 434, 2167, doi:10.1093/mnras/stt1169

  74. [80]

    , keywords =

    Kaiser, N. 1984, ApJ, 284, L9, doi:10.1086/184341 —. 1987, MNRAS, 227, 1, doi:10.1093/mnras/227.1.1

  75. [81]

    Kauffmann, G., White, S. D. M., Heckman, T. M., et al. 2004, MNRAS, 353, 713, doi:10.1111/j.1365-2966.2004.08117.x

  76. [82]

    2016, MNRAS, 457, 4340, doi:10.1093/mnras/stw248

    Klypin, A., Yepes, G., Gottlöber, S., Prada, F., & Heß, S. 2016, MNRAS, 457, 4340, doi:10.1093/mnras/stw248

  77. [83]

    1995, Phys

    Knox, L. 1995, Phys. Rev. D, 52, 4307, doi:10.1103/PhysRevD.52.4307 Kovács, A., Vielzeuf, P., Ferrero, I., et al. 2022, MNRAS, 515, 4417, doi:10. 1093/mnras/stac2011

  78. [84]

    Krolewski, A., Ferraro, S., & White, M. 2021, J. Cosmology Astropart. Phys., 2021, 028, doi:10.1088/1475-7516/2021/12/028

  79. [85]

    D., & Szalay, A

    Landy, S. D., & Szalay, A. S. 1993, ApJ, 412, 64, doi:10.1086/172900

  80. [86]

    Euclid Definition Study Report

    Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, arXiv e-prints, arXiv:1110.3193, doi:10.48550/arXiv.1110.3193

Showing first 80 references.