arxiv: 2509.17696 · v2 · submitted 2025-09-22 · 🌌 astro-ph.CO

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

Nestor Arsenov , Andras Kovacs , Mar Perez Sar , Agnes Sz. Bogdan , Francesco Sinigaglia , Francisco-Shu Kitaura , Ginevra Favole , Lyuba Slavcheva-Mihova This is my paper

Pith reviewed 2026-05-18 14:40 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords cosmic webvoidsclustersquasarsQuaialarge-scale structurehigh redshiftdensity field

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The pith

Quasars from Quaia trace 12,842 voids and 41,111 clusters in the high-redshift cosmic web.

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

The paper maps the cosmic web at redshifts 0.8 to 2.2 using positions of 708,483 quasars selected from the Quaia data set across 24,372 square degrees. Local densities are estimated via Voronoi tessellation and the REVOLVER method is applied to identify voids and clusters. The resulting catalogues are compared to 50 mock realisations, showing agreement at the 5-10 percent level in radii, inner densities and radial profiles. Largest voids reach effective radii near 250 inverse-h Mpc and clusters near 150 inverse-h Mpc, with no structures exceeding the scale of those in the mocks. The density field and both catalogues are released publicly for further use.

Core claim

In the distribution of 708,483 Quaia quasars at 0.8 < z < 2.2 we identify 12,842 voids and 41,111 clusters by means of Voronoi tessellation density estimation followed by the REVOLVER algorithm. Void and cluster radii, average inner densities and density profiles on 100 inverse-h Mpc scales agree with measurements in 50 mock catalogues at the 5-10 percent level. The largest voids reach R_eff approximately 250 inverse-h Mpc and the largest clusters 150 inverse-h Mpc, without evidence for ultra-large structures beyond those present in the mocks. Survey-mask proximity effects are present but consistent between data and simulations. The estimated density field together with the void and cluster

What carries the argument

REVOLVER void and cluster finder applied to local densities obtained from Voronoi tessellation of quasar positions.

If this is right

High-redshift large-scale structure can be traced with quasars at a precision comparable to lower-redshift galaxy surveys when the selection function is well known.
Void and cluster statistics remain consistent with the standard cosmological model as realised in the mocks.
Mask-edge effects influence detection but affect data and simulations in the same way.
The released catalogues enable new cross-correlation analyses with other high-redshift tracers.

Where Pith is reading between the lines

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

The same Voronoi-based approach could be applied to deeper or wider quasar samples to reach still higher redshifts.
Cross-correlating the identified voids and clusters with CMB lensing maps could test for integrated Sachs-Wolfe signals at z approximately 1.
Absence of ultra-large structures in both data and mocks supports homogeneity on the largest scales currently accessible at these redshifts.

Load-bearing premise

The selection function of the Quaia quasar sample is sufficiently well understood to allow accurate reconstruction of the underlying matter density field from QSO positions using Voronoi tessellation.

What would settle it

A discrepancy exceeding 10 percent in the distribution of void radii, cluster radii or inner densities between the Quaia observations and an independent set of mocks would show that the identification does not reliably recover the cosmic web.

Figures

Figures reproduced from arXiv: 2509.17696 by Agnes Sz. Bogdan, Andras Kovacs, Francesco Sinigaglia, Francisco-Shu Kitaura, Ginevra Favole, Lyuba Slavcheva-Mihova, Mar Perez Sar, Nestor Arsenov.

**Figure 1.** Figure 1: Left: the Quaia selection function which is the basis of our masking strategy, and the distribution of 4520 quasars in a narrow redshift slice at 1.8 < z < 1.81 on top. Right: redshift distribution of Quaia quasars, showing the good agreement with mocks. strain cosmological models through various probes, e.g. the void size function, density and velocity profiles, lensing effects, and also their evolution w… view at source ↗

**Figure 2.** Figure 2: A redshift slice of the Quaia catalogue at 1.0 < z < 1.03 in equatorial coordinates. Based on the Voronoi tessellation, the reconstructed local over-density (ρ/ρ¯) at the QSO positions is color-coded, and the size of the points is also proportional to their density. Pixels of low completeness are excluded from the analysis using the angular selection function. The map shows large-scale clustering of quasar… view at source ↗

**Figure 3.** Figure 3: A 2-dimensional view of the Quaia data set at 0.8 < z < 2.2 with −180◦ < RA < 180◦ , but only showing quasars with −0.5 ◦ < Dec < 0.5 ◦ . The over-density (ρ/ρ¯) color-coding and marker sizes are the same as in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Void radii (left) and cluster radii distribution (right) in the Quaia catalogue. With full colors, we show structures that are far from the mask (EdgeFlag = 0), while pale bars on top show the number of voids and clusters close to the survey edge (EdgeFlag = 1). We found good agreement when comparing the observations with the mean and standard deviation of the mocks (black and gray data points). On the mai… view at source ↗

**Figure 5.** Figure 5: Distributions of minimum density in void centres (left) and maximum density in cluster centres (right) in the Quaia catalogue. We again compare structures near and far from the survey edges, and also assess consistency between data and mocks. 0 200 400 600 800 1000 1200 1400 Number of voids Quaia, far from mask Quaia, close to mask mocks, far from mask mocks, close to mask 0 500 1000 1500 2000 2500 3000 Nu… view at source ↗

**Figure 6.** Figure 6: Distributions of average density in voids (left) and average density in clusters (right) in the Quaia catalogue. We again compare structures near and far from the survey edges, and also assess consistency between data and mocks. – Based on additional information on membership in voids and clusters provided by REVOLVER, we calculated the R/Reff relative position of each QSO in its host structure, labelled … view at source ↗

**Figure 7.** Figure 7: Distributions of the λv parameter values in voids (left) and the λc parameter values in clusters (right) in the Quaia catalogue. We again compare structures near and far from the survey edges, and also assess consistency between data and mocks. 0 100 200 300 400 500 600 Number of voids Quaia, far from mask Quaia, close to mask mocks, far from mask mocks, close to mask 0 250 500 750 1000 1250 1500 1750 2000… view at source ↗

**Figure 8.** Figure 8: Redshift distribution of voids (left) and clusters (right) in the Quaia catalogue. We again compare structures near and far from the survey edges, and also assess consistency between data and mocks. a precise measurement of the stacked density profile for tens of thousands of cosmic super-structures, which further probes the consistency between simulations and observations. We decided to use the Voronoi te… view at source ↗

**Figure 9.** Figure 9: Density profiles of voids (left) and clusters (right) in the Quaia catalogue. We again compare structures near and far from the survey edges, and also assess consistency between data (Q) and mocks (M) in the bottom panels. We show the density profiles using all voids and clusters, and we also split the catalogues into subsets with extreme values of λv and λc, as a proxy for their environment. vs. mean and … view at source ↗

read the original abstract

Understanding the formation and evolution of the cosmic web of galaxies is a fundamental goal of cosmology, using various tracers of the cosmic large-scale structure at an ever wider range of redshifts. Our principal aim is to advance the mapping of the cosmic web at high redshifts using observational and synthetic catalogues of quasars (QSOs), which offer a powerful probe of structure formation and the validity of the concordance cosmological model. In this analysis, we selected 708,483 QSOs at $0.8<z<2.2$ from the Quaia data set, allowing a reconstruction of the matter density field using 24,372 deg$^2$ sky area with a well-understood selection function, and thus going beyond previous studies. Using the REVOLVER method, we created catalogues of voids and clusters based on the estimation of the local density at QSO positions with Voronoi tessellation. We tested the consistency of Quaia data and 50 mock catalogues, including various parameters of the voids and clusters in data subsets, and also measurements of the density profiles of these cosmic super-structures at $100 h^{-1}$Mpc scales. We identified 12,842 voids and 41,111 clusters in the distribution of Quaia QSOs. The agreement between data and mocks is at a level of 5-10%, considering void and cluster radii, average inner density, and density profiles. In particular, we tested the role of survey mask proximity effects in the void and cluster detection, which albeit present, are consistent in simulations and observations. The largest voids and clusters reach $R_{eff} \approx 250 h^{-1}$Mpc and $150 h^{-1}$Mpc, respectively, but without evidence for ultra-large cosmic structures exceeding the dimensions of the largest structures in the mocks. As an important deliverable, we share our density field estimation, void catalogues, and cluster catalogues with the public, allowing various additional cross-correlation probes at high-z.

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.

Desk Editor's Note private letter to a colleague

This paper delivers new public void and cluster catalogues from the Quaia quasars at 0.8<z<2.2, with 5-10% mock agreement and a useful data release.

read the letter

This paper produces new public catalogues of voids and clusters traced by quasars from the Quaia dataset at redshifts between 0.8 and 2.2. They map the density field with Voronoi tessellation on 708,000 objects across a wide sky area and release the results for others to use. What stands out is the extension to this larger sample and the consistency tests. They compare void and cluster properties like effective radii, inner densities, and profiles at 100 Mpc/h scales against 50 mock catalogues, seeing 5-10% agreement. The checks on survey mask proximity effects also line up between the data and simulations. Making the density field and the lists of 12,842 voids and 41,111 clusters available publicly is a clear plus for follow-up work. The softer part is the selection function modeling. The approach assumes the redshift and magnitude dependence is known well enough that the local densities from QSO positions give an unbiased view of the matter field at the precision needed for these definitions. They note the function is well-understood and the mask tests are consistent, but a more explicit quantification of remaining uncertainties or a test with altered selection would make the robustness clearer. The fact that no ultra-large structures beyond the mocks appear is still a useful null result. This work is aimed at people studying the cosmic web and structure formation at high redshift using quasar tracers. Anyone needing ready catalogues for cross-correlations or further analysis will find it directly useful. It has enough substance and new data products to deserve a serious referee who can examine the details of the density reconstruction and error handling. I recommend sending it for peer review. The catalogues add concrete observational material to the field, and the validation against mocks provides a reasonable starting point even if the systematics discussion could be expanded.

Referee Report

1 major / 1 minor

Summary. The paper claims to have identified 12,842 voids and 41,111 clusters in the distribution of 708,483 Quaia QSOs at 0.8<z<2.2 over 24,372 deg² using Voronoi tessellation via the REVOLVER method to reconstruct the local density field. It reports 5-10% agreement with 50 mock catalogues in void/cluster radii, average inner densities, and 100 h^{-1}Mpc density profiles, includes tests for survey mask proximity effects, finds no evidence for ultra-large structures beyond mock expectations, and publicly releases the density field and catalogues.

Significance. If the results hold, this provides a valuable extension of cosmic web mapping to high redshifts using quasars as tracers, with the public release of the density field estimation, void catalogues, and cluster catalogues representing a clear strength for enabling further cross-correlation studies and reproducibility. The quantitative consistency checks with mocks at the 5-10% level, if robust, support the validity of standard cosmology at these epochs.

major comments (1)

[Abstract] Abstract: The central claim of 5-10% agreement between data and mocks in void/cluster properties relies on the assertion of a 'well-understood selection function' that allows accurate reconstruction of the underlying matter density field from QSO positions via Voronoi tessellation. However, the manuscript provides no quantification of residual uncertainty after selection corrections nor an explicit null test with deliberately mis-specified selection function; any unmodeled redshift-, magnitude-, or position-dependent completeness variations would systematically bias the density percentiles, directly affecting the reported counts (12,842 voids, 41,111 clusters), effective radii, inner densities, and profiles.

minor comments (1)

[Abstract] Abstract: The phrase 'various parameters of the voids and clusters in data subsets' is vague; specifying the exact parameters (e.g., radius distributions, density contrasts) and subsets (e.g., redshift bins) tested would improve clarity without altering the central results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address the major concern regarding the selection function and residual uncertainties below, and we will revise the paper accordingly to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim of 5-10% agreement between data and mocks in void/cluster properties relies on the assertion of a 'well-understood selection function' that allows accurate reconstruction of the underlying matter density field from QSO positions via Voronoi tessellation. However, the manuscript provides no quantification of residual uncertainty after selection corrections nor an explicit null test with deliberately mis-specified selection function; any unmodeled redshift-, magnitude-, or position-dependent completeness variations would systematically bias the density percentiles, directly affecting the reported counts (12,842 voids, 41,111 clusters), effective radii, inner densities, and profiles.

Authors: We thank the referee for this important observation. The selection function of the Quaia catalogue is described in detail in Storey-Fisher et al. (2024), and the 50 mock catalogues were generated to reproduce the observed redshift-, magnitude- and position-dependent completeness. The 5–10% agreement between data and mocks in void radii, inner densities and 100 h^{-1} Mpc profiles therefore provides an end-to-end consistency check on the density-field reconstruction. Nevertheless, we agree that an explicit quantification of residual uncertainty and a dedicated null test with a deliberately mis-specified selection function are not currently reported. In the revised manuscript we will add a new subsection (likely in Section 3 or 4) that (i) estimates the residual uncertainty by propagating plausible ±5% variations in completeness across redshift and magnitude bins through the Voronoi tessellation and void/cluster finding pipeline, and (ii) presents a null test in which the mocks are re-analysed after applying an intentionally incorrect selection function; the resulting shifts in void/cluster counts, radii and profiles will be quantified and compared with the observed data–mock differences. These additions will directly address the referee’s concern and will be included in the next version of the paper. revision: yes

Circularity Check

0 steps flagged

No circularity: void/cluster counts and profiles are direct outputs of applying Voronoi+REVOLVER to data and independent mocks

full rationale

The paper reconstructs the density field from 708k Quaia QSO positions via Voronoi tessellation after correcting for a modeled selection function, then runs the REVOLVER algorithm to define voids and clusters by density thresholds. The reported counts (12,842 voids, 41,111 clusters), effective radii, inner densities, and 100 h^{-1}Mpc profiles are measured on both the real catalogue and 50 independent mocks generated under standard cosmology; the 5-10% agreement is an empirical comparison rather than a self-referential prediction. No parameters are fitted to the target statistics, no self-citation supplies a uniqueness theorem or ansatz that forces the result, and the selection-function modeling is treated as an external input rather than derived from the same void/cluster analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central results depend on the accuracy of the Quaia selection function and the REVOLVER algorithm's ability to identify structures, which are taken as established in the field. Mocks assume standard Lambda-CDM cosmology.

axioms (1)

domain assumption The concordance cosmological model underlies the mock catalogues used for comparison.
Mocks are generated assuming standard Lambda-CDM cosmology to test consistency with observations.

pith-pipeline@v0.9.0 · 5941 in / 1400 out tokens · 56962 ms · 2026-05-18T14:40:35.130971+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Using the REVOLVER method, we created catalogues of voids and clusters based on the estimation of the local density at QSO positions with Voronoi tessellation.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We identified 12,842 voids and 41,111 clusters... agreement between data and mocks is at a level of 5-10%

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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Works this paper leans on

66 extracted references · 66 canonical work pages · 4 internal anchors

[1]

2025, The Open Journal of Astrophysics, 8, 42

Alonso, D., Hetmantsev, O., Fabbian, G., Slosar, A., & Storey-Fisher, K. 2025, The Open Journal of Astrophysics, 8, 42

work page 2025
[2]

C., Hložek, R., & Spergel, D

Alonso, D., Hill, J. C., Hložek, R., & Spergel, D. N. 2018, Phys. Rev. D, 97, 063514

work page 2018
[3]

2013, Living Reviews in Relativity, 16, 6

Amendola, L., Appleby, S., Bacon, D., et al. 2013, Living Reviews in Relativity, 16, 6

work page 2013
[4]

A., & Waga, I

Amendola, L., Frieman, J. A., & Waga, I. 1999, MNRAS, 309, 465

work page 1999
[5]

2024, arXiv e-prints, arXiv:2411.19531

Arsenov, N., Frey, S., Kovács, A., & Slavcheva-Mihova, L. 2024, arXiv e-prints, arXiv:2411.19531

work page arXiv 2024
[6]

2022, MNRAS, 513, 186

Aubert, M., Cousinou, M.-C., Escoffier, S., et al. 2022, MNRAS, 513, 186

work page 2022
[7]

2018, Phys

Baker, T., Clampitt, J., Jain, B., & Trodden, M. 2018, Phys. Rev. D, 98, 023511

work page 2018
[8]

Bos, E. G. P., Kitaura, F.-S., & van de Weygaert, R. 2019, MNRAS, 488, 2573

work page 2019
[9]

2013, Technical report of the Department of Statistics, University of Pennsylvania

Cai, T., Fan, J., & Jiang, T. 2013, Technical report of the Department of Statistics, University of Pennsylvania

work page 2013
[10]

2009, MNRAS, 396, 772

Cai, Y .-C., Cole, S., Jenkins, A., & Frenk, C. 2009, MNRAS, 396, 772

work page 2009
[11]

2015, MNRAS, 451, 1036

Cai, Y .-C., Padilla, N., & Li, B. 2015, MNRAS, 451, 1036

work page 2015
[12]

2024, A&A, 689, A171

Camacho-Ciurana, G., Lee, P., Arsenov, N., et al. 2024, A&A, 689, A171

work page 2024
[13]

2018, MNRAS, 476, 3195

Cautun, M., Paillas, E., Cai, Y .-C., et al. 2018, MNRAS, 476, 3195

work page 2018
[14]

2013, MNRAS, 431, 749

Clampitt, J., Cai, Y .-C., & Li, B. 2013, MNRAS, 431, 749

work page 2013
[15]

G., Raghunathan, S., Harris, K

Clowes, R. G., Raghunathan, S., Harris, K. A., et al. 2014, in Revista Mexicana de Astronomia y Astrofisica Conference Series, V ol. 44, Revista Mexicana de Astronomia y Astrofisica Conference Series, 201–201

work page 2014
[16]

M., Kitaura, F

Coloma-Nadal, J. M., Kitaura, F. S., García-Farieta, J. E., et al. 2024, J. Cosmol- ogy Astropart. Phys., 2024, 083 3 https://doi.org/10.5281/zenodo.10403370 4 https://github.com/seshnadathur/Revolver 5 https://doi.org/10.5281/zenodo.16359456

work page doi:10.5281/zenodo.10403370 2024
[17]

2021, MNRAS, 504, 5021–5038

Contarini, S., Marulli, F., Moscardini, L., et al. 2021, MNRAS, 504, 5021–5038

work page 2021
[18]

T., Cautun, M., Giblin, B., et al

Davies, C. T., Cautun, M., Giblin, B., et al. 2021, MNRAS, 507, 2267

work page 2021
[19]

Delchambre, L., Bailer-Jones, C. A. L., Bellas-Velidis, I., et al. 2023, A&A, 674, A31

work page 2023
[20]

A., Veyrat, D., & BenZvi, S

Douglass, K. A., Veyrat, D., & BenZvi, S. 2023, ApJS, 265, 7

work page 2023
[21]

J., & Einasto, M

Einasto, J., Hütsi, G., Suhhonenko, I., Liivamägi, L. J., & Einasto, M. 2021, A&A, 647, A17

work page 2021
[22]

2025, arXiv e-prints, arXiv:2504.20992

Fabbian, G., Alonso, D., Storey-Fisher, K., & Cornish, T. 2025, arXiv e-prints, arXiv:2504.20992

work page arXiv 2025
[23]

2019, MN- RAS, 490, 3573 Forero Sánchez, D., Kitaura, F

Fang, Y ., Hamaus, N., Jain, B., Pandey, S., & DES Collaboration. 2019, MN- RAS, 490, 3573 Forero Sánchez, D., Kitaura, F. S., Sinigaglia, F., Coloma-Nadal, J. M., & Kneib, J. P. 2024, J. Cosmology Astropart. Phys., 2024, 001 Gaia Collaboration, Bailer-Jones, C. A. L., Teyssier, D., et al. 2023a, A&A, 674, A41 Gaia Collaboration, Vallenari, A., Brown, A. ...

work page 2019
[24]

M., Hivon, E., Banday, A

Gorski, K. M., Hivon, E., Banday, A. J., et al. 2005, The Astrophysical Journal, 622, 759

work page 2005
[25]

R., Neyrinck, M

Granett, B. R., Neyrinck, M. C., & Szapudi, I. 2008, ApJL, 683, L99

work page 2008
[26]

2021, Euclid: Forecasts from redshift- space distortions and the Alcock-Paczynski test with cosmic voids

Hamaus, N., Aubert, M., Pisani, A., et al. 2021, Euclid: Forecasts from redshift- space distortions and the Alcock-Paczynski test with cosmic voids

work page 2021
[27]

M., et al

Hamaus, N., Pisani, A., Sutter, P. M., et al. 2016, Phys. Rev. Lett., 117, 091302

work page 2016
[28]

J., Granett, B

Hawken, A. J., Granett, B. R., Iovino, A., et al. 2017, A&A, 607, A54

work page 2017
[29]

G., et al

Horvath, I., Bagoly, Z., Balazs, L. G., et al. 2025, Universe, 11, 121 Ili´c, S., Langer, M., & Douspis, M. 2013, A&A, 556, A51

work page 2025
[30]

E., et al

Kitaura, F.-S., Ata, M., Angulo, R. E., et al. 2016, MNRAS, 457, L113

work page 2016
[31]

Kitaura, F. S. & Hess, S. 2013, MNRAS, 435, L78

work page 2013
[32]

S., Yepes, G., & Prada, F

Kitaura, F. S., Yepes, G., & Prada, F. 2014, MNRAS, 439, L21 Kovács, A., Beck, R., Smith, A., et al. 2022, MNRAS, 513, 15 Kovács, A., Jeffrey, N., Gatti, M., et al. 2022, MNRAS, 510, 216 Kovács, A., Sánchez, C., García-Bellido, J., & the DES collaboration. 2017, MN- RAS, 465, 4166 Kovács, A., Sánchez, C., García-Bellido, J., & the DES collaboration. 2019,...

work page 2014
[33]

2013, ApJ, 762, L20

Krause, E., Chang, T.-C., Doré, O., & Umetsu, K. 2013, ApJ, 762, L20

work page 2013
[34]

The DESI Experiment, a whitepaper for Snowmass 2013

Levi, M., Bebek, C., Beers, T., et al. 2013, ArXiv e-prints: 1308.0847 [arXiv:1308.0847]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[35]

2024, MNRAS, 527, 2663

Li, G., Ma, Y .-Z., Tramonte, D., & Li, G.-L. 2024, MNRAS, 527, 2663

work page 2024
[36]

I., van de Weygaert, R., Cautun, M., et al

Libeskind, N. I., van de Weygaert, R., Cautun, M., et al. 2018, MNRAS, 473, 1195

work page 2018
[37]

2024, A&A, 683, A130

Liu, A., Bulbul, E., Kluge, M., et al. 2024, A&A, 683, A130

work page 2024
[38]

LSST Science Book, Version 2.0

Lopez, A. M., Clowes, R. G., & Williger, G. M. 2022, MNRAS, 516, 1557 LSST Science Collaboration, Abell, P. A., Allison, J., et al. 2009, ArXiv e-prints [arXiv:0912.0201]

work page internal anchor Pith review Pith/arXiv arXiv 2022
[39]

A., Scherrer, R

Mao, Q., Berlind, A. A., Scherrer, R. J., et al. 2017, ApJ, 835, 161

work page 2017
[40]

2013, MNRAS, 434, 398

Nadathur, S. 2013, MNRAS, 434, 398

work page 2013
[41]

2016, MNRAS, 461, 358

Nadathur, S. 2016, MNRAS, 461, 358

work page 2016
[42]

M., Percival, W

Nadathur, S., Carter, P. M., Percival, W. J., Winther, H. A., & Bautista, J. E. 2019, Physical Review D, 100, 023504

work page 2019
[43]

& Crittenden, R

Nadathur, S. & Crittenden, R. 2016, ApJ, 830, L19

work page 2016
[44]

2014, Phys

Nadathur, S., Lavinto, M., Hotchkiss, S., & Räsänen, S. 2014, Phys. Rev. D, 90, 103510

work page 2014
[45]

2020, MNRAS, 491, 1709

Naidoo, K., Whiteway, L., Massara, E., et al. 2020, MNRAS, 491, 1709

work page 2020
[46]

Neyrinck, M. C. 2008, MNRAS, 386, 2101

work page 2008
[47]

2015, Journal of Korean Astronomical Society, 48, 75

Park, C., Song, H., Einasto, M., Lietzen, H., & Heinamaki, P. 2015, Journal of Korean Astronomical Society, 48, 75

work page 2015
[48]

Piccirilli, G., Fabbian, G., Alonso, D., et al. 2024, J. Cosmology Astropart. Phys., 2024, 012

work page 2024
[49]

N., et al

Pisani, A., Massara, E., Spergel, D. N., et al. 2019, Cosmic voids: a novel probe to shed light on our Universe

work page 2019
[50]

M., Hamaus, N., et al

Pisani, A., Sutter, P. M., Hamaus, N., et al. 2015, Phys. Rev. D, 92, 083531 Planck Collaboration, Aghanim, N., Akrami, Y ., et al. 2020, A&A, 641, A6

work page 2015
[51]

2016, PKDGRA V3: Beyond Trillion Particle Cosmological Simulations for the Next Era of Galaxy Surveys Rácz, G., Kiessling, A., Csabai, I., & Szapudi, I

Potter, D., Stadel, J., & Teyssier, R. 2016, PKDGRA V3: Beyond Trillion Particle Cosmological Simulations for the Next Era of Galaxy Surveys Rácz, G., Kiessling, A., Csabai, I., & Szapudi, I. 2023, A&A, 672, A59

work page 2016
[52]

D., & Whitehorn, N

Raghunathan, S., Nadathur, S., Sherwin, B. D., & Whitehorn, N. 2020, ApJ, 890, 168

work page 2020
[53]

2025, ApJ, 982, 38

Rincon, H., Benzvi, S., Douglass, K., et al. 2025, ApJ, 982, 38

work page 2025
[54]

Sachs, R. K. & Wolfe, A. M. 1967, ApJL, 147, 73 Sánchez, C., Clampitt, J., Kovács, A., & et al. 2017, MNRAS, 465, 746

work page 1967
[55]

2024, arXiv e-prints, arXiv:2412.02761

Sartori, S., Vielzeuf, P., Escoffier, S., et al. 2024, arXiv e-prints, arXiv:2412.02761

work page arXiv 2024
[56]

S., et al

Sawala, T., Teeriaho, M., Frenk, C. S., et al. 2025, MNRAS, 541, L22

work page 2025
[57]

2023, MNRAS, 526, 4978

Schaye, J., Kugel, R., Schaller, M., et al. 2023, MNRAS, 526, 4978

work page 2023
[58]

2019, Journal of Cosmology and Astroparticle Physics, 2019, 055–055

Schuster, N., Hamaus, N., Pisani, A., et al. 2019, Journal of Cosmology and Astroparticle Physics, 2019, 055–055

work page 2019
[59]

In preparation

Sinigaglia, F. & Kitaura, F.-S. 2025, "In preparation" Article number, page 11 of 12 A&A proofs:manuscript no. arxive

work page 2025
[60]

2022, ApJ, 927, 230

Sinigaglia, F., Kitaura, F.-S., Balaguera-Antolínez, A., et al. 2022, ApJ, 927, 230

work page 2022
[61]

Fast and accurate Gaia-unWISE quasar mock catalogs from LPT and Eulerian bias

Sinigaglia, F., Kitaura, F.-S., Shiferaw, M., et al. 2025 [arXiv:2509.15890]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[62]

W., Rix, H.-W., et al

Storey-Fisher, K., Hogg, D. W., Rix, H.-W., et al. 2024, ApJ, 964, 69

work page 2024
[63]

The Dark Energy Survey

Takahashi, R., Hamana, T., Shirasaki, M., et al. 2017, ApJ, 850, 24 The Dark Energy Survey Collaboration. 2005, arXiv:astro-ph/0510346 [arXiv:astro-ph/0510346]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[64]

M., & Storey-Fisher, K

Veronesi, N., van Velzen, S., Rossi, E. M., & Storey-Fisher, K. 2025, MNRAS, 536, 375

work page 2025
[65]

Vielzeuf, P., Calabrese, M., Carbone, C., Fabbian, G., & Baccigalupi, C. 2023, J. Cosmology Astropart. Phys., 2023, 010

work page 2023
[66]

J., et al

Yuan, S., Zhang, H., Ross, A. J., et al. 2024, MNRAS, 530, 947 Article number, page 12 of 12

work page 2024