Why Cosmic Voids Matter: Pristine Evolution

Alice Pisani; Jochen Weller; Klaus Dolag; Nico Hamaus; Nico Schuster

REVIEW 2 major objections 5 minor 4 cited by

Why Cosmic Voids Matter: Pristine Evolution

T0 review · 2 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Halo-defined cosmic voids stabilize below redshift 1, their evolution set by cosmic expansion and described by linear growth.

desk verdict A well-executed simulation study with a genuinely new relative-size framework; the stabilization claim is plausible but needs a quantitative test, and the rank-conservation interpretation is overstated. read the letter →

arxiv 2509.07092 v1 pith:JEBST6QG submitted 2025-09-08 astro-ph.CO

Nico Schuster , Nico Hamaus , Alice Pisani , Klaus Dolag , Jochen Weller This is my paper

classification astro-ph.CO

keywords cosmicvoidsvoidevolutionlineargrowthfactorhalobiassizefunctiondensityprofilesdarkenergyhydrodynamicalsimulations

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Using hydrodynamical simulations from redshift 5.04 to the present, the paper argues that halo-defined cosmic voids—voids carved out by the galaxy-halo population—can only be compared across cosmic time if they are binned by their rank (percentile by radius) within their contemporary void population, not by absolute size. In that relative framework, the apparent 'inverse' evolution of halo void density profiles disappears and is revealed as a selection effect of the evolving void size function amplified by halo bias. The central physical claim is that the halo void population stabilizes below z ≃ 1: comoving density profiles, size functions, and core densities align, meaning later evolution is driven by cosmic expansion rather than ongoing halo formation. Around these stable voids, the surrounding dark-matter density field follows linear growth theory, with deviations only as nonlinear growth in small voids and suppressed growth in the largest voids. If right, late-time voids are predictable, passive tracers of expansion, which is exactly what dark-energy probes from upcoming surveys need.

What carries the argument

The two load-bearing tools are (1) a relative size framework—each redshift's voids are ranked by effective radius and split into quartiles (or quintiles), so equal-count bins compare voids of the same contemporary rank instead of the same physical size—and (2) the linear growth factor D+(a), applied backwards from a low-redshift baseline via δ(x,z) = D̂(z,z*) δ(x,z*) to predict the evolving matter profiles around halo voids. The rank binning removes the selection effect created by the evolving void size function; the backward growth prediction isolates where linear theory holds.

What would settle it

In a simulation with saved particle IDs, track individual halo voids across snapshots and check whether voids at the same radius percentile at z=1 and z=0 are the same objects or their descendants; if percentile membership shuffles severely between epochs, the reported stabilization is an artifact of percentile rebinning.

Watch

Extended reading notes

Core claim

The paper's central discovery is that a void's properties are tied more fundamentally to its rank within its contemporary population than to its absolute size. Comparing voids of fixed comoving radius across redshifts mixes populations because the void size function evolves strongly—CDM voids merge and grow while halo voids fragment into more numerous smaller voids as new halos form. For halo voids this mixing produces an apparent inverse evolution of density profiles (compensation walls seemingly shrinking over time) that is a tracer-selection artifact, amplified by halo bias, not physical. Restacking profiles in quartile bins of the contemporary radius distribution removes the artifact and

Load-bearing premise

That a void's rank (percentile by radius) among its contemporaries is a stable identity marker across cosmic time, so that stacking by rank at different redshifts compares the same underlying voids even though individual voids cannot be tracked.

Editorial extensions

If this is right

Analyses of halo-void density profiles and lensing signals should bin voids by percentile of the contemporary radius distribution; fixed comoving-radius bins will otherwise mix populations and mimic inverse evolution.
Below z ≃ 1 the halo-void population acts as a passive tracer of cosmic expansion, so its stacked profiles can be predicted from a low-redshift baseline with linear growth theory.
Deviations from linear growth are localized: nonlinear wall growth around small voids and suppressed growth in the largest voids, so the residuals themselves could be used to test dark energy or modified gravity.
The self-similarity across simulation resolutions implies the same evolutionary stages—fragmentation, then stabilization—occur at scales and epochs set by the tracer population, allowing results from one tracer or halo-mass regime to be scaled to another.
For weak lensing and the Alcock-Paczynski test, the close agreement between predicted and measured matter profiles around stable voids provides a clean theoretical baseline across a wide redshift range.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The rank-conservation premise is testable: in a simulation with particle-ID tracking, one could verify that the same descendant voids occupy the same radius percentile across snapshots; without that, the stabilization could be a rebinning artifact (the paper itself notes individual halo voids cannot be tracked).
If the stabilization is physical, the comoving void size function for low-mass-halo tracers should become nearly time-independent below z ≈ 1, a direct prediction for spectroscopic surveys.
The suppressed growth seen in the largest voids implies a scale-dependent effective growth rate inside voids relative to their walls; void-galaxy redshift-space distortions or stacked lensing at two redshifts could detect it.
The same relative-size recipe may clean up other void statistics where inverse trends appear, such as massive-neutrino or modified-gravity analyses, by removing the population-mixing selection effect before interpreting the physics.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Let me cut to the chase. The useful idea here is that you should bin halo voids by percentile in radius rather than by absolute comoving size when comparing across redshifts. Fixed-size bins mix different populations because the halo void size function evolves a lot; percentile bins don't, and the figures make that concrete. The CDM density around the same voids evolves as expected even when the halo profiles show the spurious inverse trend, which is the strongest evidence that the effect is selection, not physics. The linear growth test is clean: D+(a) from the background cosmology, baseline profile taken from the simulation at z_min, no fitted parameters, backward prediction. Deviations are small and scale-dependent in the expected places. That is a genuinely parameter-free test, and it works. Credit also for openly discussing that the backward prediction underestimates errors, so their residual plots are the conservative case. The code and data are public.

Where are the soft spots? The headline claim that a void's properties are tied to rank rather than absolute size is an over-interpretation. What they actually show is that rank-based bins remove the selection effect caused by the evolving size function. They admit in Section 5.1 that individual halo voids cannot be reliably tracked, and they never test whether rank is conserved. I don't think the paper needs individual tracking—population statistics are the point—but the phrase 'more fundamentally tied to rank' implies a physical identity that isn't demonstrated. At late times, when the VSF stabilizes, rank and size are equivalent, so the stabilization claim is less affected; at early times, the rank bins are still a reasonable way to compare like-with-like evolutionary stages, supported by self-similarity across resolutions. Still, the authors should either test rank conservation statistically or soften the language.

The bigger mechanical gap is that the claimed stabilization (z<1) is evaluated by eye. The VSF plots show overlap, the profile plots show overlap, but there is no quantitative measure of when the distributions stop evolving. A Kolmogorov-Smirnov test on the VSF or profile residuals across adjacent redshifts would make the claim solid. The missing error bars on the VSF are minor, and the dark-energy interpretation of suppressed growth in large voids is speculative but explicitly labeled as such.

Bottom line: this is a solid, useful paper. The relative-size framework will be adopted by people working with DESI and Euclid. It deserves peer review, with requests for a quantitative stabilization metric and a more careful statement about what rank means. I would cite it for the framework and the linear growth result, and I'd bring it to reading group.

Referee Report

2 major / 5 minor

Summary. The paper uses the Magneticum hydrodynamical simulations (midres, highres, ultra-hr) to study the evolution of voids identified in CDM and halo tracers from z = 5.04 to z = 0. The main claims are: (i) a relative size framework (stacking by radius percentile rather than by fixed comoving radius) is necessary to avoid selection effects caused by the evolving void size function; (ii) within this framework, the halo-void population stabilizes at z ≲ 1, with evolution driven by cosmic expansion rather than by ongoing halo formation; and (iii) the CDM density around halo voids is remarkably well described by linear growth theory, with deviations on small scales (non-linear growth) and in the largest voids (suppressed growth, possibly due to dark energy). The paper supports these claims with multi-resolution comparisons, a tracer-selection test (halo vs. CDM profiles around the same voids), and a parameter-free linear-growth prediction using the background cosmology's D+(a).

Significance. If the main claims hold, the paper provides a practical framework for analyzing voids in upcoming surveys (DESI, Euclid, Roman): it identifies a regime where halo-void properties are stable and where matter profiles can be predicted from linear theory without free parameters. The relative-size framework is a potentially useful methodological contribution that could mitigate known selection effects. Strengths include the use of multiple simulation resolutions, the explicit comparison of halo and CDM tracers around the same voids (Figures 7 and 8), and the public release of the profile code and data. The linear-growth prediction is genuinely parameter-free: D+(a) is computed from the assumed WMAP7 cosmology (Eq. 6.1) and the baseline profile is taken directly from simulation, leaving no fitted parameters. However, the central interpretation that a void's rank in the contemporary population is a conserved, physically meaningful identifier is not directly tested, and the quantitative linear-growth comparison in the evolving-population section has a coordinate-mapping subtlety that needs clarification.

major comments (2)

[§5.2, Figs. 9-10] The paper's central claim that a void's properties are 'more fundamentally tied to its rank within its contemporary population than to its absolute size' rests on the assumption that a fixed radius percentile at different redshifts selects the same underlying population. This assumption is not tested. Section 5.1 explicitly states that 'individual halo voids cannot be reliably tracked over time,' and voids are re-identified independently at each snapshot. If voids merge or fragment, a fixed percentile at z=1 and z=0 may contain different objects, and the apparent late-time alignment of profiles in r/r_v may be a consequence of the percentile normalization (equal numbers per bin by construction) rather than a physical freeze. The authors should provide evidence that rank tracks a conserved population property—for example, by matching voids across snapshots with the CDM density field, by s
[§6.1, Eq. (6.2), Figs. 11-12] The linear-growth prediction is formulated in Eq. (6.2) for density contrast as a function of comoving coordinate x: δ(x,z) = D̂(z,z⋆) δ(x,z⋆). However, Figures 11 and 12 show profiles and predictions versus r/r_v, while voids are re-identified at each redshift and have different r_v distributions. The paper does not state how the baseline profile at z_min is mapped to the radial coordinate of a different void population at higher z. If the same r/r_v bin is simply multiplied by D̂, the prediction is not the linear-theory prediction for the same physical region, because r_v evolves with redshift (as seen in the evolving VSF, Figure 3). This affects the quantitative claim of agreement at the |Δρ/ρ̄| ≲ 0.05 level, especially for z > 1 where r_v changes substantially. The authors should either clarify the coordinate mapping (e.g., show that r_v is constant for matched populations in the red

minor comments (5)

[§4.2, Fig. 3] The text states that the comoving VSF aligns 'almost perfectly at redshifts z ≲ 1.32' for highres, but the snapshots shown are z = 0.25, 0.29, 0.47, 0.67, 0.90, 1.18, and 1.98. There is no snapshot at z = 1.32; please clarify whether 1.32 is an interpolated value or a typo.
[§6.1, Figs. 11-12] The residuals in the lower panels are described as 'data - prediction,' but the text says the backward method 'slightly underestimates the errors of the predictions,' making the plots a worst-case scenario. This is fine as a caveat, but it should be stated clearly in the figure captions so readers interpret the residuals correctly.
[§6.1, Fig. 12] The interpretation of the 'suppressed growth in the largest voids' as 'potentially driven by the influence of dark energy' is speculative and not tested in this work. The authors should label this explicitly as a hypothesis, not a conclusion, and perhaps suggest a concrete test (e.g., running a simulation with a different dark-energy model).
[§5.3, velocity profiles] The velocity-profile analysis is mentioned only in prose ('While not depicted in this work'). Since the paper makes claims about the 'turning point' and the balance between outflow and new halo formation, it would be helpful to include at least one figure or to explain why these profiles are omitted.
[§3.2, Table 2] The definition of Θ(r_j) uses two Heaviside functions, but the notation is a bit terse. It would help to define the bin edges explicitly as r − δr and r + δr, and to state that δr is a constant fraction of r_v.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the linear-growth prediction is parameter-free and falsifiable, and the relative-size framework is an empirical comparison rather than a definitional result.

full rationale

The paper's central derivations do not reduce to their own inputs. The linear-growth test (Sec. 6, Eqs. 6.1 and 6.2) computes D+(a) from the fixed WMAP7 ΛCDM background and uses a measured baseline profile at z_min as input; no parameter is fitted to the predicted redshifts. The backward prediction is genuine extrapolation, and the paper explicitly reports deviations (non-linear growth in small voids, suppressed growth in the largest voids), so the test is falsifiable and not forced. The relative-size framework (Sec. 5.2) divides voids into radius percentiles at each redshift; the observed alignment of profiles across redshifts is an empirical finding, not guaranteed by the binning. The authors further test robustness to the number of bins and to tracer choice. The statement in Sec. 5.1 that 'individual halo voids cannot be reliably tracked over time' is an acknowledged limitation on interpreting rank bins as a conserved population, but it does not make any step circular. Self-citations to [80, 81] are used for profile-estimation methods and prior context; the new conclusions are supported by Magneticum measurements and comparisons, not imported by citation. No uniqueness theorem is invoked, and no fitted quantity is relabeled as a prediction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The analysis uses standard cosmological assumptions and the Magneticum simulations. The free parameters are selection choices (mass cuts, merging threshold, subsampling) rather than fitted parameters. The self-similarity assumption is the most paper-specific axiom.

free parameters (3)

Halo mass cut M_h = 1e12 Msun/h (midres), 1e11 Msun/h (highres)
Hand-chosen thresholds to ensure well-resolved tracers; directly affects which voids are identified and the inferred stabilization epochs (z≲0.67 in mr, z≲1.32 in hr). Section 4.1, Figure 1.
VIDE merging threshold = 1e-9
Set to the VIDE default to prevent void merging; determines the void catalog and thus all derived statistics. Section 3.1.
CDM subsampling fraction for void identification = 0.066% of CDM particles in mr, 0.034% in hr
Fixed to match halo number density at z=0.29; sets the physical scale of CDM voids and affects the comparison with halo voids. Section 4.1, Figure 2.

assumptions (4)

domain assumption Flat ΛCDM cosmology with WMAP7 parameters (Ω_m=0.272, Ω_Λ=0.728, h=0.704, σ_8=0.809, n_s=0.963)
The Magneticum simulations are run under this cosmology; all results are conditional on it. Section 2.
standard math Linear growth factor D+(a) from Eq. (6.1) accurately describes the homogeneous background growth of density perturbations
Used for the backward predictions in Section 6. This is a standard result from linear perturbation theory in ΛCDM.
domain assumption Hydrodynamic simulations provide a faithful representation of the nonlinear matter distribution for void statistics
The analysis relies on Magneticum as a proxy for the universe, including its baryonic and AGN feedback models. Section 2.
ad hoc to paper Void populations are self-similar across resolutions and mass cuts
The relative framework relies on the claim that different resolutions probe the same evolutionary stages at different epochs. This is asserted from visual comparison of Figures 3-10 and not proven quantitatively. Section 5.3.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Why Cosmic Voids Matter: Pristine Evolution." pith.science (2026). https://pith.science/paper/JEBST6QG

@misc{pith2026250907092,
  author       = {Pith},
  title        = {Pith review of: Why Cosmic Voids Matter: Pristine Evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JEBST6QG}},
  note         = {Machine review of arXiv:2509.07092}
}

abstract

We utilize the Magneticum suite of hydrodynamical simulations to investigate the formation and evolution of cosmic voids from $z = 5.04$ to present day, using cold dark matter and (sub-) halo tracers in high-density samples. This includes the evolution of their global properties, such as size, shape, inner density, and average density, as well as their radial density profiles. Our results provide several key conclusions for void analyses in modern surveys. We demonstrate that a relative size framework is required, mitigating methodological selection effects and revealing the true physical evolution of densities around halo-defined voids. This necessity arises from our findings that a void's properties are more fundamentally tied to its rank within its contemporary population than to its absolute size. Using this framework, we show that the evolution of halo voids stabilizes at redshifts below $z \simeq 1$, driven primarily by cosmic expansion rather than ongoing halo formation. We further find that the matter evolution around these stable voids is remarkably well-described by linear growth theory, with deviations appearing as non-linear growth on small scales and suppressed growth in the largest voids, potentially driven by the influence of dark energy. This late-time stability and the predictable evolution confirm voids as pristine laboratories for probing the nature of dark energy with upcoming surveys.

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

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

Baryons in the Darkest Sites of the Universe
astro-ph.CO 2026-05 unverdicted novelty 7.0 of 10

Stacking 3455 CHIME/FRB sightlines on 1288 SDSS voids shows a 3.2 sigma DM deficit toward centers, implying 60 percent baryon underdensity consistent with galaxy underdensity and hydrodynamical simulations.
Optimization of Tessellation-based Statistics: Void Statistics
astro-ph.CO 2026-06 unverdicted novelty 5.0 of 10

Subsampling and averaging stabilizes Delaunay and Voronoi tessellation void statistics (VSF, VTCF, VPS), reducing scatters attributed to tessellation instabilities and boosting BAO signal-to-noise and cosmological con...
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 of 10

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.
Towards precision cosmology with Voids x CMB correlations (I): Roman-Agora mock catalogs and pipeline validation
astro-ph.CO 2025-12 unverdicted novelty 5.0 of 10

The authors introduce analog matching to generate Roman Space Telescope mock catalogs that reproduce emission-line galaxy statistics and highlight the need to match void properties separately from two-point clustering...

Reference graph

Works this paper leans on

160 extracted references · 40 canonical work pages · cited by 4 Pith papers

[1]

Gregory and L.A

S.A. Gregory and L.A. Thompson,The Coma/A1367 supercluster and its environs., Astrophys. J.222(1978) 784

1978
[2]

J˜ oeveer, J

M. J˜ oeveer, J. Einasto and E. Tago,Spatial distribution of galaxies and of clusters of galaxies in the southern galactic hemisphere, Mon. Not. Roy. Astron. Soc.185(1978) 357

1978
[3]

Kirshner, J

R.P. Kirshner, J. Oemler, A., P.L. Schechter and S.A. Shectman,A million cubic megaparsec void in Bootes ?, Astrophys. J.248(1981) L57

1981
[4]

Zeldovich, J

I.B. Zeldovich, J. Einasto and S.F. Shandarin,Giant voids in the Universe, Nature300 (1982) 407

1982
[5]

Bertschinger,The self-similar evolution of holes in an Einstein-de Sitter universe, ApJS58 (1985) 1

E. Bertschinger,The self-similar evolution of holes in an Einstein-de Sitter universe, ApJS58 (1985) 1

1985
[6]

van de Weygaert and E

R. van de Weygaert and E. van Kampen,Voids in Gravitational Instability Scenarios - Part One - Global Density and Velocity Fields in an Einstein - De-Sitter Universe, Mon. Not. Roy. Astron. Soc.263(1993) 481

1993
[7]

Bennett, M

C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon et al.,First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results, ApJS148(2003) 1 [astro-ph/0302207]

arXiv 2003
[8]

Aghanim, Y

Planck Collaboration, N. Aghanim, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont et al., Planck 2018 results. I. Overview and the cosmological legacy of Planck, Astron. Astrophys. 641(2020) A1 [1807.06205]

arXiv 2018

Show all 160 references

[9]

Riess, A.V

A.G. Riess, A.V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P.M. Garnavich et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, AJ116(1998) 1009 [astro-ph/9805201]

1998 arXiv
[10]

Perlmutter, G

S. Perlmutter, G. Aldering, G. Goldhaber, R.A. Knop, P. Nugent, P.G. Castro et al., Measurements ofΩandΛfrom 42 High-Redshift Supernovae, Astrophys. J.517(1999) 565 [astro-ph/9812133]

1999 arXiv
[11]

Adame, J

A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander, M. Alvarez et al.,DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations, JCAP 2025(2025) 021 [2404.03002]

2024 arXiv
[12]

Adame, J

A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander, C. Allende Prieto et al.,DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements, JCAP2025(2025) 028 [2411.12022]

2024 arXiv
[13]

Abdul-Karim, J

DESI Collaboration, M. Abdul-Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen et al.,DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints, arXiv e-prints(2025) arXiv:2503.14738 [2503.14738]

2025 arXiv
[14]

Sloan Digital Sky Survey (http://www.sdss3.org/)
[15]

Dawson, D.J

K.S. Dawson, D.J. Schlegel, C.P. Ahn, S.F. Anderson, ´E. Aubourg, S. Bailey et al.,The Baryon Oscillation Spectroscopic Survey of SDSS-III, AJ145(2013) 10 [1208.0022]

2013 arXiv
[16]

The Dark Energy Survey Collaboration,The Dark Energy Survey,arXiv e-prints(2005) astro [astro-ph/0510346]. – 30 –

2005 arXiv
[17]

Dawson, J.-P

K.S. Dawson, J.-P. Kneib, W.J. Percival, S. Alam, F.D. Albareti, S.F. Anderson et al.,The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data, AJ 151(2016) 44 [1508.04473]

2016 arXiv
[18]

Pisani, E

A. Pisani, E. Massara, D.N. Spergel, D. Alonso, T. Baker, Y.-C. Cai et al.,Cosmic voids: a novel probe to shed light on our Universe, BAAS51(2019) 40 [1903.05161]

2019 arXiv
[19]

Moresco, L

M. Moresco, L. Amati, L. Amendola, S. Birrer, J.P. Blakeslee, M. Cantiello et al.,Unveiling the Universe with emerging cosmological probes,Living Reviews in Relativity25(2022) 6 [2201.07241]

2022 arXiv
[20]

Di Valentino, J.L

E. Di Valentino, J.L. Said, A. Riess, A. Pollo, V. Poulin, A. G´ omez-Valent et al.,The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics,Physics of the Dark Universe49(2025) 101965

2025
[21]

Cai and M

Y.-C. Cai and M. Neyrinck,Cosmology with Cosmic Voids,arXiv e-prints(2025) arXiv:2503.22532 [2503.22532]

2025 arXiv
[22]

Biswas, E

R. Biswas, E. Alizadeh and B.D. Wandelt,Voids as a precision probe of dark energy, Phys. Rev. D82(2010) 023002 [1002.0014]

2010 arXiv
[23]

Pan, M.S

D.C. Pan, M.S. Vogeley, F. Hoyle, Y.-Y. Choi and C. Park,Cosmic voids in Sloan Digital Sky Survey Data Release 7, Mon. Not. Roy. Astron. Soc.421(2012) 926 [1103.4156]

2012 arXiv
[24]

Lavaux and B.D

G. Lavaux and B.D. Wandelt,Precision Cosmography with Stacked Voids, Astrophys. J.754 (2012) 109 [1110.0345]

2012 arXiv
[25]

Sutter, G

P.M. Sutter, G. Lavaux, B.D. Wandelt and D.H. Weinberg,A First Application of the Alcock-Paczynski Test to Stacked Cosmic Voids, Astrophys. J.761(2012) 187 [1208.1058]

2012 arXiv
[26]

Hamaus, B.D

N. Hamaus, B.D. Wandelt, P.M. Sutter, G. Lavaux and M.S. Warren,Cosmology with Void-Galaxy Correlations, Phys. Rev. Lett.112(2014) 041304 [1307.2571]

2014 arXiv
[27]

Pisani, P.M

A. Pisani, P.M. Sutter, N. Hamaus, E. Alizadeh, R. Biswas, B.D. Wandelt et al.,Counting voids to probe dark energy, Phys. Rev. D92(2015) 083531 [1503.07690]

2015 arXiv
[28]

Mao, A.A

Q. Mao, A.A. Berlind, R.J. Scherrer, M.C. Neyrinck, R. Scoccimarro, J.L. Tinker et al., Cosmic Voids in the SDSS DR12 BOSS Galaxy Sample: The Alcock-Paczynski Test, Astrophys. J.835(2017) 160 [1602.06306]

2017 arXiv
[29]

Hamaus, M.-C

N. Hamaus, M.-C. Cousinou, A. Pisani, M. Aubert, S. Escoffier and J. Weller,Multipole analysis of redshift-space distortions around cosmic voids, JCAP7(2017) 014 [1705.05328]

2017 arXiv
[30]

Sahl´ en,Cluster-void degeneracy breaking: Neutrino properties and dark energy, Phys

M. Sahl´ en,Cluster-void degeneracy breaking: Neutrino properties and dark energy, Phys. Rev. D99(2019) 063525 [1807.02470]

2019 arXiv
[31]

Nadathur, A

S. Nadathur, A. Woodfinden, W.J. Percival, M. Aubert, J. Bautista, K. Dawson et al.,The completed SDSS-IV extended baryon oscillation spectroscopic survey: geometry and growth from the anisotropic void-galaxy correlation function in the luminous red galaxy sample, Mon. Not. Ro...

2020 arXiv
[32]

Hamaus, A

N. Hamaus, A. Pisani, J.-A. Choi, G. Lavaux, B.D. Wandelt and J. Weller,Precision cosmology with voids in the final BOSS data, JCAP2020(2020) 023 [2007.07895]

2020 arXiv
[33]

Correa, D.J

C.M. Correa, D.J. Paz, A.G. S´ anchez, A.N. Ruiz, N.D. Padilla and R.E. Angulo, Redshift-space effects in voids and their impact on cosmological tests. Part I: the void size function, Mon. Not. Roy. Astron. Soc.500(2021) 911 [2007.12064]

2021 arXiv
[34]

Davies, M

C.T. Davies, M. Cautun, B. Giblin, B. Li, J. Harnois-D´ eraps and Y.-C. Cai,Constraining cosmology with weak lensing voids, Mon. Not. Roy. Astron. Soc.507(2021) 2267 [2010.11954]. – 31 –

2021
[35]

Vielzeuf, A

P. Vielzeuf, A. Kov´ acs, U. Demirbozan, P. Fosalba, E. Baxter, N. Hamaus et al.,Dark Energy Survey Year 1 results: the lensing imprint of cosmic voids on the cosmic microwave background, Mon. Not. Roy. Astron. Soc.500(2021) 464 [1911.02951]

2021 arXiv
[36]

Aubert, M.-C

M. Aubert, M.-C. Cousinou, S. Escoffier, A.J. Hawken, S. Nadathur, S. Alam et al.,The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: growth rate of structure measurement from cosmic voids, Mon. Not. Roy. Astron. Soc.513(2022) 186 [2007.09013]

2022 arXiv
[37]

Kov´ acs, P

A. Kov´ acs, P. Vielzeuf, I. Ferrero, P. Fosalba, U. Demirbozan, R. Miquel et al.,Dark Energy Survey Year 3 results: Imprints of cosmic voids and superclusters in the Planck CMB lensing map, Mon. Not. Roy. Astron. Soc.515(2022) 4417 [2203.11306]

2022 arXiv
[38]

Sheth and R

R.K. Sheth and R. van de Weygaert,A hierarchy of voids: much ado about nothing, Mon. Not. Roy. Astron. Soc.350(2004) 517 [astro-ph/0311260]

2004 arXiv
[39]

Conroy, A.L

C. Conroy, A.L. Coil, M. White, J.A. Newman, R. Yan, M.C. Cooper et al.,The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics from z ˜1 to z ˜0, Astrophys. J.635 (2005) 990 [astro-ph/0508250]

2005 arXiv
[40]

Jennings, Y

E. Jennings, Y. Li and W. Hu,The abundance of voids and the excursion set formalism, Mon. Not. Roy. Astron. Soc.434(2013) 2167 [1304.6087]

2013 arXiv
[41]

Nadathur,Testing cosmology with a catalogue of voids in the BOSS galaxy surveys, Mon

S. Nadathur,Testing cosmology with a catalogue of voids in the BOSS galaxy surveys, Mon. Not. Roy. Astron. Soc.461(2016) 358 [1602.04752]

2016 arXiv
[42]

Sahl´ en,´I

M. Sahl´ en,´I. Zubeld ´ ıa and J. Silk,Cluster-Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void, Astrophys. J.820(2016) L7 [1511.04075]

2016 arXiv
[43]

Contarini, T

S. Contarini, T. Ronconi, F. Marulli, L. Moscardini, A. Veropalumbo and M. Baldi, Cosmological exploitation of the size function of cosmic voids identified in the distribution of biased tracers, Mon. Not. Roy. Astron. Soc.488(2019) 3526 [1904.01022]

2019 arXiv
[44]

Verza, A

G. Verza, A. Pisani, C. Carbone, N. Hamaus and L. Guzzo,The void size function in dynamical dark energy cosmologies, JCAP2019(2019) 040 [1906.00409]

2019 arXiv
[45]

Contarini, A

S. Contarini, A. Pisani, N. Hamaus, F. Marulli, L. Moscardini and M. Baldi,Cosmological Constraints from the BOSS DR12 Void Size Function, Astrophys. J.953(2023) 46 [2212.03873]

2023 arXiv
[46]

Verza, G

G. Verza, G. Degni, A. Pisani, N. Hamaus, E. Massara, A. Benson et al.,Cosmology with voids from the Nancy Grace Roman Space Telescope,arXiv e-prints(2024) arXiv:2410.19713 [2410.19713]

2024
[47]

Hamaus, P.M

N. Hamaus, P.M. Sutter and B.D. Wandelt,Universal Density Profile for Cosmic Voids, Physical Review Letters112(2014) 251302 [1403.5499]

2014 arXiv
[48]

Pisani, G

A. Pisani, G. Lavaux, P.M. Sutter and B.D. Wandelt,Real-space density profile reconstruction of stacked voids, Mon. Not. Roy. Astron. Soc.443(2014) 3238 [1306.3052]

2014 arXiv
[49]

Y.-C. Cai, A. Taylor, J.A. Peacock and N. Padilla,Redshift-space distortions around voids, Mon. Not. Roy. Astron. Soc.462(2016) 2465 [1603.05184]

2016 arXiv
[50]

Hamaus, A

N. Hamaus, A. Pisani, P.M. Sutter, G. Lavaux, S. Escoffier, B.D. Wandelt et al.,Constraints on Cosmology and Gravity from the Dynamics of Voids,Physical Review Letters117(2016) 091302 [1602.01784]

2016 arXiv
[51]

Hawken, B.R

A.J. Hawken, B.R. Granett, A. Iovino, L. Guzzo, J.A. Peacock, S. de la Torre et al.,The VIMOS Public Extragalactic Redshift Survey. Measuring the growth rate of structure around cosmic voids, Astron. Astrophys.607(2017) A54 [1611.07046]

2017 arXiv
[52]

Achitouv,New constraints on the linear growth rate using cosmic voids in the SDSS DR12 datasets, Phys

I. Achitouv,New constraints on the linear growth rate using cosmic voids in the SDSS DR12 datasets, Phys. Rev. D100(2019) 123513 [1903.05645]. – 32 –

2019 arXiv
[53]

Correa, D.J

C.M. Correa, D.J. Paz, N.D. Padilla, A.N. Ruiz, R.E. Angulo and A.G. S´ anchez,Non-fiducial cosmological test from geometrical and dynamical distortions around voids, Mon. Not. Roy. Astron. Soc.485(2019) 5761 [1811.12251]

2019 arXiv
[54]

Hawken, M

A.J. Hawken, M. Aubert, A. Pisani, M.-C. Cousinou, S. Escoffier, S. Nadathur et al., Constraints on the growth of structure around cosmic voids in eBOSS DR14, JCAP2020 (2020) 012 [1909.04394]

2020 arXiv
[55]

Correa, D.J

C.M. Correa, D.J. Paz, N.D. Padilla, A.G. S´ anchez, A.N. Ruiz and R.E. Angulo, Redshift-space effects in voids and their impact on cosmological tests - II. The void-galaxy cross-correlation function, Mon. Not. Roy. Astron. Soc.509(2022) 1871 [2107.01314]

2022 arXiv
[56]

Hamaus, M

N. Hamaus, M. Aubert, A. Pisani, S. Contarini, G. Verza, M.C. Cousinou et al.,Euclid: Forecasts from redshift-space distortions and the Alcock-Paczynski test with cosmic voids, Astron. Astrophys.658(2022) A20 [2108.10347]

2022 arXiv
[57]

Woodfinden, S

A. Woodfinden, S. Nadathur, W.J. Percival, S. Radinovic, E. Massara and H.A. Winther, Measurements of cosmic expansion and growth rate of structure from voids in the Sloan Digital Sky Survey between redshift 0.07 and 1.0, Mon. Not. Roy. Astron. Soc.516(2022) 4307 [2205.06258]

2022 arXiv
[58]

Radinovi´ c, S

S. Radinovi´ c, S. Nadathur, H.A. Winther, W.J. Percival, A. Woodfinden, E. Massara et al., Euclid: Cosmology forecasts from the void-galaxy cross-correlation function with reconstruction, Astron. Astrophys.677(2023) A78 [2302.05302]

2023 arXiv
[59]

Krause, T.-C

E. Krause, T.-C. Chang, O. Dor´ e and K. Umetsu,The Weight of Emptiness: The Gravitational Lensing Signal of Stacked Voids, Astrophys. J.762(2013) L20 [1210.2446]

2013 arXiv
[60]

Clampitt and B

J. Clampitt and B. Jain,Lensing measurements of the mass distribution in SDSS voids, Mon. Not. Roy. Astron. Soc.454(2015) 3357 [1404.1834]

2015 arXiv
[61]

Chantavat, U

T. Chantavat, U. Sawangwit and B.D. Wandelt,Void Profile from Planck Lensing Potential Map, Astrophys. J.836(2017) 156 [1702.01009]

2017 arXiv
[62]

Y.-C. Cai, M. Neyrinck, Q. Mao, J.A. Peacock, I. Szapudi and A.A. Berlind,The lensing and temperature imprints of voids on the cosmic microwave background, Mon. Not. Roy. Astron. Soc.466(2017) 3364 [1609.00301]

2017 arXiv
[63]

S´ anchez, J

C. S´ anchez, J. Clampitt, A. Kovacs, B. Jain, J. Garc ´ ıa-Bellido, S. Nadathur et al.,Cosmic voids and void lensing in the Dark Energy Survey Science Verification data, Mon. Not. Roy. Astron. Soc.465(2017) 746 [1605.03982]

2017 arXiv
[64]

Baker, J

T. Baker, J. Clampitt, B. Jain and M. Trodden,Void lensing as a test of gravity, Phys. Rev. D98(2018) 023511 [1803.07533]

2018 arXiv
[65]

Y. Fang, N. Hamaus, B. Jain, S. Pandey, G. Pollina, C. S´ anchez et al.,Dark Energy Survey year 1 results: the relationship between mass and light around cosmic voids, Mon. Not. Roy. Astron. Soc.490(2019) 3573 [1909.01386]

2019 arXiv
[66]

Bonici, C

M. Bonici, C. Carbone, S. Davini, P. Vielzeuf, L. Paganin, V. Cardone et al.,Euclid: Forecasts from the void-lensing cross-correlation, Astron. Astrophys.670(2023) A47 [2206.14211]

2023 arXiv
[67]

Martin, M.J

H.L. Martin, M.J. Hudson, A. Woodfinden, L. Baumont, T. de Boer, P.A. Burger et al., Lensing without mass: The matter density profile in cosmic voids from UNIONS,arXiv e-prints(2025) arXiv:2507.13450 [2507.13450]

2025
[68]

Hamaus, P.M

N. Hamaus, P.M. Sutter, G. Lavaux and B.D. Wandelt,Testing cosmic geometry without dynamic distortions using voids, JCAP12(2014) 013 [1409.3580]

2014 arXiv
[69]

K.C. Chan, N. Hamaus and V. Desjacques,Large-scale clustering of cosmic voids, Phys. Rev. D90(2014) 103521 [1409.3849]. – 33 –

2014 arXiv
[70]

Chuang, F.-S

C.-H. Chuang, F.-S. Kitaura, Y. Liang, A. Font-Ribera, C. Zhao, P. McDonald et al.,Linear redshift space distortions for cosmic voids based on galaxies in redshift space, Phys. Rev. D95 (2017) 063528 [1605.05352]

2017 arXiv
[71]

Kreisch, A

C.D. Kreisch, A. Pisani, C. Carbone, J. Liu, A.J. Hawken, E. Massara et al.,Massive Neutrinos Leave Fingerprints on Cosmic Voids, Mon. Not. Roy. Astron. Soc. (2019) 1877 [1808.07464]

2019 arXiv
[72]

Voivodic, H

R. Voivodic, H. Rubira and M. Lima,The halo void (dust) model of large scale structure, Journal of Cosmology and Astroparticle Physics2020(2020) 033

2020
[73]

Kreisch, A

C.D. Kreisch, A. Pisani, F. Villaescusa-Navarro, D.N. Spergel, B.D. Wandelt, N. Hamaus et al.,The GIGANTES Data Set: Precision Cosmology from Voids in the Machine-learning Era, Astrophys. J.935(2022) 100 [2107.02304]

2022 arXiv
[74]

B.Y. Wang, A. Pisani, F. Villaescusa-Navarro and B.D. Wandelt,Machine-learning Cosmology from Void Properties, Astrophys. J.955(2023) 131 [2212.06860]

2023 arXiv
[75]

Thiele, E

L. Thiele, E. Massara, A. Pisani, C. Hahn, D.N. Spergel, S. Ho et al.,Neutrino Mass Constraint from an Implicit Likelihood Analysis of BOSS Voids, Astrophys. J.969(2024) 89 [2307.07555]

2024 arXiv
[76]

Wang and A

B.Y. Wang and A. Pisani,Cosmology from One Galaxy in a Void?, Astrophys. J.970(2024) L32 [2405.04447]

2024 arXiv
[77]

Fraser, E

T.S. Fraser, E. Paillas, W.J. Percival, S. Nadathur, S. Radinovi´ c and H.A. Winther,Modelling the BOSS void-galaxy cross-correlation function using a neural-network emulator, JCAP2025 (2025) 001 [2407.03221]

2025 arXiv
[78]

Lehman, N

K. Lehman, N. Schuster, L. Lucie-Smith, N. Hamaus, C.T. Davies and K. Dolag, Cosmological Inference with Cosmic Voids and Neural Network Emulators,arXiv e-prints (2025) arXiv:2502.05262 [2502.05262]

2025
[79]

Salcedo, A

A.N. Salcedo, A. Pisani and N. Hamaus,Multi-probe cosmology forecasts from HOD-based forward modeling of galaxy and void statistics,arXiv e-prints(2025) arXiv:2504.08221 [2504.08221]

2025 arXiv
[80]

Schuster, N

N. Schuster, N. Hamaus, K. Dolag and J. Weller,Why cosmic voids matter: nonlinear structure & linear dynamics, JCAP2023(2023) 031 [2210.02457]

2023 arXiv
[81]

Schuster, N

N. Schuster, N. Hamaus, K. Dolag and J. Weller,Why cosmic voids matter: mitigation of baryonic physics, JCAP2024(2024) 065 [2312.11241]

2024 arXiv
[82]

Stopyra, H.V

S. Stopyra, H.V. Peiris and A. Pontzen,How to build a catalogue of linearly evolving cosmic voids, Mon. Not. Roy. Astron. Soc.500(2021) 4173 [2007.14395]

2021 arXiv
[83]

Lepinzan, C.T

M.D. Lepinzan, C.T. Davies, T. Castro, N. Schuster, J. Mohr and P. Monaco,Tracing Cosmic Voids with fast simulations,arXiv e-prints(2025) arXiv:2506.19506 [2506.19506]

2025 arXiv
[84]

Massara, F

E. Massara, F. Villaescusa-Navarro, M. Viel and P.M. Sutter,Voids in massive neutrino cosmologies, JCAP11(2015) 018 [1506.03088]

2015 arXiv
[85]

Banerjee and N

A. Banerjee and N. Dalal,Simulating nonlinear cosmological structure formation with massive neutrinos, JCAP11(2016) 015 [1606.06167]

2016 arXiv
[86]

Schuster, N

N. Schuster, N. Hamaus, A. Pisani, C. Carbone, C.D. Kreisch, G. Pollina et al.,The bias of cosmic voids in the presence of massive neutrinos, JCAP2019(2019) 055 [1905.00436]

2019 arXiv
[87]

Zhang, Z

G. Zhang, Z. Li, J. Liu, D.N. Spergel, C.D. Kreisch, A. Pisani et al.,Void halo mass function: A promising probe of neutrino mass, Phys. Rev. D102(2020) 083537 [1910.07553]

2020 arXiv
[88]

Contarini, F

S. Contarini, F. Marulli, L. Moscardini, A. Veropalumbo, C. Giocoli and M. Baldi,Cosmic voids in modified gravity models with massive neutrinos, Mon. Not. Roy. Astron. Soc.504 (2021) 5021 [2009.03309]. – 34 –

2021 arXiv
[89]

Bayer, F

A.E. Bayer, F. Villaescusa-Navarro, E. Massara, J. Liu, D.N. Spergel, L. Verde et al., Detecting Neutrino Mass by Combining Matter Clustering, Halos, and Voids, Astrophys. J. 919(2021) 24 [2102.05049]

2021 arXiv
[90]

Zivick, P.M

P. Zivick, P.M. Sutter, B.D. Wandelt, B. Li and T.Y. Lam,Using cosmic voids to distinguish f(R) gravity in future galaxy surveys, Mon. Not. Roy. Astron. Soc.451(2015) 4215 [1411.5694]

2015 arXiv
[91]

Y.-C. Cai, N. Padilla and B. Li,Testing gravity using cosmic voids, Mon. Not. Roy. Astron. Soc.451(2015) 1036 [1410.1510]

2015 arXiv
[92]

Barreira, M

A. Barreira, M. Cautun, B. Li, C.M. Baugh and S. Pascoli,Weak lensing by voids in modified lensing potentials, JCAP8(2015) 028 [1505.05809]

2015 arXiv
[93]

Falck, K

B. Falck, K. Koyama, G.-B. Zhao and M. Cautun,Using voids to unscreen modified gravity, Mon. Not. Roy. Astron. Soc.475(2018) 3262 [1704.08942]

2018 arXiv
[94]

Paillas, M

E. Paillas, M. Cautun, B. Li, Y.-C. Cai, N. Padilla, J. Armijo et al.,The Santiago-Harvard-Edinburgh-Durham void comparison II: unveiling the Vainshtein screening using weak lensing, Mon. Not. Roy. Astron. Soc.484(2019) 1149 [1810.02864]

2019 arXiv
[95]

Davies, M

C.T. Davies, M. Cautun and B. Li,Cosmological test of gravity using weak lensing voids, Mon. Not. Roy. Astron. Soc.490(2019) 4907 [1907.06657]

2019 arXiv
[96]

Perico, R

E.L.D. Perico, R. Voivodic, M. Lima and D.F. Mota,Cosmic voids in modified gravity scenarios, Astron. Astrophys.632(2019) A52

2019
[97]

Wilson and R

C. Wilson and R. Bean,Testing f (R ) gravity with scale dependent cosmic void velocity profiles, Phys. Rev. D104(2021) 023512 [2012.05925]

2021 arXiv
[98]

Tamosiunas, C

A. Tamosiunas, C. Briddon, C. Burrage, A. Cutforth, A. Moss and T. Vincent,Chameleon screening in cosmic voids, JCAP2022(2022) 056 [2206.06480]

2022 arXiv
[99]

Fiorini, K

B. Fiorini, K. Koyama and A. Izard,Studying large-scale structure probes of modified gravity with COLA, JCAP2022(2022) 028 [2208.01345]

2022 arXiv
[100]

Williams, H.J

M.J. Williams, H.J. Macpherson, D.L. Wiltshire and C. Stevens,First investigation of void statistics in numerical relativity simulations, Mon. Not. Roy. Astron. Soc.536(2025) 2645 [2403.15134]

2025 arXiv
[101]

Yang, M.C

L.F. Yang, M.C. Neyrinck, M.A. Arag´ on-Calvo, B. Falck and J. Silk,Warmth elevating the depths: shallower voids with warm dark matter, Mon. Not. Roy. Astron. Soc.451(2015) 3606 [1411.5029]

2015 arXiv
[102]

D.S. Reed, A. Schneider, R.E. Smith, D. Potter, J. Stadel and B. Moore,The same with less: the cosmic web of warm versus cold dark matter dwarf galaxies, Mon. Not. Roy. Astron. Soc. 451(2015) 4413 [1410.1541]

2015 arXiv
[103]

Baldi and F

M. Baldi and F. Villaescusa-Navarro,Cosmic degeneracies - II. Structure formation in joint simulations of warm dark matter and f(R) gravity, Mon. Not. Roy. Astron. Soc.473(2018) 3226

2018
[104]

Lester and K

E. Lester and K. Bolejko,Imprints of decaying dark matter on cosmic voids, Phys. Rev. D 104(2021) 123540 [2111.11593]

2021 arXiv
[105]

Arcari, E

S. Arcari, E. Pinetti and N. Fornengo,Got plenty of nothing: cosmic voids as a probe of particle dark matter, JCAP2022(2022) 011 [2205.03360]

2022 arXiv
[106]

Lester and K

E. Lester and K. Bolejko,Constraining decaying dark matter models with gravitational lensing and cosmic voids, Phys. Rev. D112(2025) 023546 [2507.08275]

2025 arXiv
[107]

K.C. Chan, N. Hamaus and M. Biagetti,Constraint of void bias on primordial non-Gaussianity, Phys. Rev. D99(2019) 121304 [1812.04024]. – 35 –

2019 arXiv
[108]

van de Weygaert,Voids and the Cosmic Web: cosmic depression & spatial complexity, in The Zeldovich Universe: Genesis and Growth of the Cosmic Web, R

R. van de Weygaert,Voids and the Cosmic Web: cosmic depression & spatial complexity, in The Zeldovich Universe: Genesis and Growth of the Cosmic Web, R. van de Weygaert, S. Shandarin, E. Saar and J. Einasto, eds., vol. 308, pp. 493–523, Oct., 2016, DOI [1611.01222]

2016 arXiv
[109]

Gallagher and P

A. Gallagher and P. Coles,Evolution of Cosmic Voids in the Schr¨ odinger-Poisson Formalism, The Open Journal of Astrophysics5(2022) 17 [2208.13851]

2022 arXiv
[110]

Piza˜ na, J.C

F.A. Piza˜ na, J.C. Hidalgo, I.D. Gaspar and R.A. Sussman,Growth rate of spherical voids with non-comoving dark matter and baryons,Classical and Quantum Gravity41(2024) 015013 [2306.02668]

2024 arXiv
[111]

Bromley and M.J

B.C. Bromley and M.J. Geller,Cosmology with voids, JCAP2025(2025) 011 [2407.03882]

2025 arXiv
[112]

Ceccarelli, D

L. Ceccarelli, D. Paz, M. Lares, N. Padilla and D.G. Lambas,Clues on void evolution - I. Large-scale galaxy distributions around voids, Mon. Not. Roy. Astron. Soc.434(2013) 1435 [1306.5798]

2013 arXiv
[113]

D. Paz, M. Lares, L. Ceccarelli, N. Padilla and D.G. Lambas,Clues on void evolution-II. Measuring density and velocity profiles on SDSS galaxy redshift space distortions, Mon. Not. Roy. Astron. Soc.436(2013) 3480 [1306.5799]

2013 arXiv
[114]

Ruiz, D.J

A.N. Ruiz, D.J. Paz, M. Lares, H.E. Luparello, L. Ceccarelli and D.G. Lambas,Clues on void evolution - III. Structure and dynamics in void shells, Mon. Not. Roy. Astron. Soc.448 (2015) 1471 [1501.02120]

2015 arXiv
[115]

Cautun, R

M. Cautun, R. van de Weygaert, B.J.T. Jones and C.S. Frenk,Evolution of the cosmic web, Mon. Not. Roy. Astron. Soc.441(2014) 2923 [1401.7866]

2014 arXiv
[116]

Sutter, P

P.M. Sutter, P. Elahi, B. Falck, J. Onions, N. Hamaus, A. Knebe et al.,The life and death of cosmic voids, Mon. Not. Roy. Astron. Soc.445(2014) 1235 [1403.7525]

2014 arXiv
[117]

Wojtak, D

R. Wojtak, D. Powell and T. Abel,Voids in cosmological simulations over cosmic time, Mon. Not. Roy. Astron. Soc.458(2016) 4431 [1602.08541]

2016 arXiv
[118]

Adermann, P.J

E. Adermann, P.J. Elahi, G.F. Lewis and C. Power,Cosmic voids in evolving dark sector cosmologies: the high-redshift universe, Mon. Not. Roy. Astron. Soc.479(2018) 4861 [1807.02938]

2018 arXiv
[119]

Massara and R.K

E. Massara and R.K. Sheth,Density and velocity profiles around cosmic voids,arXiv e-prints (2018) arXiv:1811.03132 [1811.03132]

2018 arXiv
[120]

Vall´ es-P´ erez, V

D. Vall´ es-P´ erez, V. Quilis and S. Planelles,Void Replenishment: How Voids Accrete Matter Over Cosmic History, Astrophys. J.920(2021) L2 [2109.08165]

2021 arXiv
[121]

Verza, C

G. Verza, C. Carbone, A. Pisani and A. Renzi,DEMNUni: disentangling dark energy from massive neutrinos with the void size function, JCAP2023(2023) 044 [2212.09740]

2023 arXiv
[122]

Curtis, B

O. Curtis, B. McDonough and T.G. Brainerd,Density Profiles of TNG 300 Voids across Cosmic Time, Astrophys. J.985(2025) 244 [2504.15902]

2025 arXiv
[123]

Abdul-Karim, A.G

DESI Collaboration, M. Abdul-Karim, A.G. Adame, D. Aguado, J. Aguilar, S. Ahlen et al., Data Release 1 of the Dark Energy Spectroscopic Instrument,arXiv e-prints(2025) arXiv:2503.14745 [2503.14745]

2025 arXiv
[124]

Rincon, S

H. Rincon, S. Benzvi, K. Douglass, D. Veyrat, J.N. Aguilar, S. Ahlen et al.,DESIV AST: Catalogs of Low-redshift Voids Using Data from the DESI Data Release 1 Bright Galaxy Survey, Astrophys. J.982(2025) 38 [2411.00148]

2025 arXiv
[125]

Contarini, G

S. Contarini, G. Verza, A. Pisani, N. Hamaus, M. Sahl´ en, C. Carbone et al.,Euclid: Cosmological forecasts from the void size function, Astron. Astrophys.667(2022) A162 [2205.11525]. – 36 –

2022 arXiv
[126]

Dor´ e, M.W

O. Dor´ e, M.W. Werner, M.L.N. Ashby, L.E. Bleem, J. Bock, J. Burt et al.,Science Impacts of the SPHEREx All-Sky Optical to Near-Infrared Spectral Survey II: Report of a Community Workshop on the Scientific Synergies Between the SPHEREx Survey and Other Astronomy Observatories...

2018 arXiv
[127]

Hirschmann, K

M. Hirschmann, K. Dolag, A. Saro, L. Bachmann, S. Borgani and A. Burkert,Cosmological simulations of black hole growth: AGN luminosities and downsizing, Mon. Not. Roy. Astron. Soc.442(2014) 2304 [1308.0333]

2014 arXiv
[128]

Dolag, B.M

K. Dolag, B.M. Gaensler, A.M. Beck and M.C. Beck,Constraints on the distribution and energetics of fast radio bursts using cosmological hydrodynamic simulations, Mon. Not. Roy. Astron. Soc.451(2015) 4277 [1412.4829]

2015 arXiv
[129]

Steinborn, K

L.K. Steinborn, K. Dolag, M. Hirschmann, M.A. Prieto and R.-S. Remus,A refined sub-grid model for black hole accretion and AGN feedback in large cosmological simulations, Mon. Not. Roy. Astron. Soc.448(2015) 1504 [1409.3221]

2015 arXiv
[130]

Teklu, R.-S

A.F. Teklu, R.-S. Remus, K. Dolag, A.M. Beck, A. Burkert, A.S. Schmidt et al.,Connecting Angular Momentum and Galactic Dynamics: The Complex Interplay between Spin, Mass, and Morphology, Astrophys. J.812(2015) 29 [1503.03501]

2015 arXiv
[131]

Bocquet, A

S. Bocquet, A. Saro, K. Dolag and J.J. Mohr,Halo mass function: baryon impact, fitting formulae, and implications for cluster cosmology, Mon. Not. Roy. Astron. Soc.456(2016) 2361 [1502.07357]

2016 arXiv
[132]

Dolag, E

K. Dolag, E. Komatsu and R. Sunyaev,SZ effects in the Magneticum Pathfinder simulation: comparison with the Planck, SPT, and ACT results, Mon. Not. Roy. Astron. Soc.463(2016) 1797 [1509.05134]

2016 arXiv
[133]

Remus, K

R.-S. Remus, K. Dolag and T. Hoffmann,The Outer Halos of Very Massive Galaxies: BCGs and their DSC in the Magneticum Simulations,Galaxies5(2017) 49 [1709.02393]

2017 arXiv
[134]

Castro, M

T. Castro, M. Quartin, C. Giocoli, S. Borgani and K. Dolag,The effect of baryons in the cosmological lensing PDFs, Mon. Not. Roy. Astron. Soc.478(2018) 1305 [1711.10017]

2018 arXiv
[135]

Castro, S

T. Castro, S. Borgani, K. Dolag, V. Marra, M. Quartin, A. Saro et al.,On the impact of baryons on the halo mass function, bias, and cluster cosmology, Mon. Not. Roy. Astron. Soc. 500(2021) 2316 [2009.01775]

2021
[136]

Angelinelli, S

M. Angelinelli, S. Ettori, K. Dolag, F. Vazza and A. Ragagnin,Mapping ‘out-of-the-box’ the properties of the baryons in massive halos, Astron. Astrophys.663(2022) L6 [2206.08382]

2022 arXiv
[137]

Dolag, R.-S

K. Dolag, R.-S. Remus, L.M. Valenzuela, L.C. Kimmig, B. Seidel, S. Fortune et al., Encyclopedia Magneticum: Scaling Relations from Cosmic Dawn to Present Day,arXiv e-prints(2025) arXiv:2504.01061 [2504.01061]

2025
[138]

Komatsu, K.M

E. Komatsu, K.M. Smith, J. Dunkley, C.L. Bennett, B. Gold, G. Hinshaw et al.,Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, ApJS192(2011) 18 [1001.4538]

2011 arXiv
[139]

Springel,The cosmological simulation code GADGET-2, Mon

V. Springel,The cosmological simulation code GADGET-2, Mon. Not. Roy. Astron. Soc.364 (2005) 1105 [astro-ph/0505010]

2005 arXiv
[140]

A.M. Beck, G. Murante, A. Arth, R.S. Remus, A.F. Teklu, J.M.F. Donnert et al.,An improved SPH scheme for cosmological simulations, Mon. Not. Roy. Astron. Soc.455(2016) 2110 [1502.07358]

2016 arXiv
[141]

Dolag, E

K. Dolag, E. Mevius and R.-S. Remus,Distribution and Evolution of Metals in the Magneticum Simulations,Galaxies5(2017) 35 [1708.00027]

2017 arXiv
[142]

Springel, T

V. Springel, T. Di Matteo and L. Hernquist,Modelling feedback from stars and black holes in galaxy mergers, Mon. Not. Roy. Astron. Soc.361(2005) 776 [astro-ph/0411108]. – 37 –

2005 arXiv
[143]

Di Matteo, V

T. Di Matteo, V. Springel and L. Hernquist,Energy input from quasars regulates the growth and activity of black holes and their host galaxies, Nature433(2005) 604 [astro-ph/0502199]

2005 arXiv
[144]

Fabjan, S

D. Fabjan, S. Borgani, L. Tornatore, A. Saro, G. Murante and K. Dolag,Simulating the effect of active galactic nuclei feedback on the metal enrichment of galaxy clusters, Mon. Not. Roy. Astron. Soc.401(2010) 1670 [0909.0664]

2010 arXiv
[145]

Pollina, N

G. Pollina, N. Hamaus, K. Dolag, J. Weller, M. Baldi and L. Moscardini,On the linearity of tracer bias around voids, Mon. Not. Roy. Astron. Soc.469(2017) 787 [1610.06176]

2017 arXiv
[146]

Pollina, N

G. Pollina, N. Hamaus, K. Paech, K. Dolag, J. Weller, C. S´ anchez et al.,On the relative bias of void tracers in the Dark Energy Survey, Mon. Not. Roy. Astron. Soc.487(2019) 2836 [1806.06860]

2019 arXiv
[147]

Pelliciari, S

D. Pelliciari, S. Contarini, F. Marulli, L. Moscardini, C. Giocoli, G.F. Lesci et al.,Exploring the cosmological synergy between galaxy cluster and cosmic void number counts, Mon. Not. Roy. Astron. Soc.522(2023) 152 [2210.07248]

2023 arXiv
[148]

Springel, S.D.M

V. Springel, S.D.M. White, G. Tormen and G. Kauffmann,Populating a cluster of galaxies - I. Results at [formmu2]z=0, Mon. Not. Roy. Astron. Soc.328(2001) 726 [astro-ph/0012055]

2001 arXiv
[149]

Dolag, S

K. Dolag, S. Borgani, G. Murante and V. Springel,Substructures in hydrodynamical cluster simulations, Mon. Not. Roy. Astron. Soc.399(2009) 497 [0808.3401]

2009 arXiv
[150]

Sutter, G

P.M. Sutter, G. Lavaux, N. Hamaus, A. Pisani, B.D. Wandelt, M. Warren et al.,VIDE: The Void IDentification and Examination toolkit,Astronomy and Computing9(2015) 1 [1406.1191]

2015 arXiv
[151]

Neyrinck,ZOBOV: a parameter-free void-finding algorithm, Mon

M.C. Neyrinck,ZOBOV: a parameter-free void-finding algorithm, Mon. Not. Roy. Astron. Soc.386(2008) 2101 [0712.3049]

2008 arXiv
[152]

Platen, R

E. Platen, R. van de Weygaert and B.J.T. Jones,A cosmic watershed: the WVF void detection technique, Mon. Not. Roy. Astron. Soc.380(2007) 551 [0706.2788]

2007 arXiv
[153]

Verza, C

G. Verza, C. Carbone and A. Renzi,The Halo Bias inside Cosmic Voids, Astrophys. J.940 (2022) L16 [2207.04039]

2022 arXiv
[154]

Dodelson and F

S. Dodelson and F. Schmidt,Modern Cosmology, Academic Press (2020), 10.1016/C2017-0-01943-2

2020 doi
[155]

Melchior, P.M

P. Melchior, P.M. Sutter, E.S. Sheldon, E. Krause and B.D. Wandelt,First measurement of gravitational lensing by cosmic voids in SDSS, Mon. Not. Roy. Astron. Soc.440(2014) 2922 [1309.2045]

2014 arXiv
[156]

Davies, M

C.T. Davies, M. Cautun and B. Li,Weak lensing by voids in weak lensing maps, Mon. Not. Roy. Astron. Soc.480(2018) L101 [1803.08717]

2018 arXiv
[157]

Jeffrey, M

N. Jeffrey, M. Gatti, C. Chang, L. Whiteway, U. Demirbozan, A. Kovacs et al.,Dark Energy Survey Year 3 results: Curved-sky weak lensing mass map reconstruction, Mon. Not. Roy. Astron. Soc.505(2021) 4626 [2105.13539]

2021 arXiv
[158]

Hunter,Matplotlib: A 2d graphics environment,Computing in Science & Engineering9 (2007) 90

J.D. Hunter,Matplotlib: A 2d graphics environment,Computing in Science & Engineering9 (2007) 90

2007
[159]

Harris, K.J

C.R. Harris, K.J. Millman, S.J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau et al.,Array programming with NumPy,Nature585(2020) 357

2020
[160]

Virtanen, R

P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau et al., SciPy 1.0: fundamental algorithms for scientific computing in python,Nature Methods17 (2020) 261. – 38 –

2020

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [1]

Gregory and L.A

S.A. Gregory and L.A. Thompson,The Coma/A1367 supercluster and its environs., Astrophys. J.222(1978) 784

1978

[2] [2]

J˜ oeveer, J

M. J˜ oeveer, J. Einasto and E. Tago,Spatial distribution of galaxies and of clusters of galaxies in the southern galactic hemisphere, Mon. Not. Roy. Astron. Soc.185(1978) 357

1978

[3] [3]

Kirshner, J

R.P. Kirshner, J. Oemler, A., P.L. Schechter and S.A. Shectman,A million cubic megaparsec void in Bootes ?, Astrophys. J.248(1981) L57

1981

[4] [4]

Zeldovich, J

I.B. Zeldovich, J. Einasto and S.F. Shandarin,Giant voids in the Universe, Nature300 (1982) 407

1982

[5] [5]

Bertschinger,The self-similar evolution of holes in an Einstein-de Sitter universe, ApJS58 (1985) 1

E. Bertschinger,The self-similar evolution of holes in an Einstein-de Sitter universe, ApJS58 (1985) 1

1985

[6] [6]

van de Weygaert and E

R. van de Weygaert and E. van Kampen,Voids in Gravitational Instability Scenarios - Part One - Global Density and Velocity Fields in an Einstein - De-Sitter Universe, Mon. Not. Roy. Astron. Soc.263(1993) 481

1993

[7] [7]

Bennett, M

C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon et al.,First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results, ApJS148(2003) 1 [astro-ph/0302207]

arXiv 2003

[8] [8]

Aghanim, Y

Planck Collaboration, N. Aghanim, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont et al., Planck 2018 results. I. Overview and the cosmological legacy of Planck, Astron. Astrophys. 641(2020) A1 [1807.06205]

arXiv 2018