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Void spin distribution as a powerful probe of $\sigma_{8}$

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper presents numerical evidence that the distribution of cosmic void spins is a sensitive and nearly exclusive probe of $\sigma_8$, with a 10% change in $\sigma_8$ shifting the best-fit generalized Gamma parameters by…

desk verdict A credible proof-of-concept for void spins as a sigma8 probe, but the independence from halo-mass selection is not yet demonstrated. read the letter →

arxiv 2501.09476 v2 pith:4XFO7MJG submitted 2025-01-16 astro-ph.CO

Geonwoo Kang , Jounghun Lee (Seoul National University) This is my paper · ORCID
classification astro-ph.CO
keywords cosmicvoidsvoidspinsigma8generalizedGammadistributioncosmologicalparameterdegeneracyN-bodysimulationslarge-scalestructure
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

The paper offers a numerical proof of concept that how fast cosmic voids spin can pin down $\sigma_8$, the amplitude of matter fluctuations smoothed on $8\,h^{-1}\mathrm{Mpc}$ scales. From 15 dark-matter-only simulations that differ from the fiducial $\Lambda$CDM cosmology in only one parameter at a time, the authors measure the distribution of void spin magnitudes and fit it with a generalized Gamma curve with two parameters, $k$ and $\theta$. A 10% shift in $\sigma_8$ moves the best-fit $(k,\theta)$ by roughly 4$\sigma$, while comparable shifts in $\Omega_{\rm cdm}h^2$, $M_\nu$, and $w$ leave the curve nearly unchanged. The authors also show, using only galaxy redshifts, that a stacked blueshift/redshift asymmetry can reveal the projected void spin, making the statistic observable in principle. If the sensitivity survives real data, void spins would offer a rare probe of $\sigma_8$ that is not entangled with the usual degeneracies.

What carries the argument

The central object is the dimensionless void spin vector, defined as the specific angular momentum of a void's member halos treated as equal-mass point particles: $$\mathbf{j} \equiv \frac{1}{\sqrt{2}(V_v R_{\rm eff})}\sum_i (\mathbf{x}_i - \mathbf{x}_c) \times (\mathbf{v}_i - \mathbf{v}_c),$$ with magnitude $j = |\mathbf{j}|$. The carrying mechanism is the two-parameter generalized Gamma distribution fit to the measured $p(j)$; the parameter distance $D$ between fits from different cosmologies, with errors propagated from the $\chi^2$ covariance, quantifies how distinguishable two models are. The analytic fit turns the whole shape of the spin distribution into a compact two-dimensional fingerprint, and the $\chi^2$ contours in $(k,\theta)$ space are what reveal the strong $\sigma_8$ dependence and weak dependence on the other three parameters. Voids are selected with a fixed minimum radius, a halo mass threshold of $10^{11.5}\,h^{-1}M_\odot$, and a member-halo number cut of 15 before constructing the distributions.

What would settle it

Compute the void spin distribution from the same simulations after conditioning on or regressing out void halo mass, for example by matching the halo mass distributions across $\sigma_8$ models before comparing $p(j)$; if the residual shift in $\{k,\theta\}$ drops below 4$\sigma$, the claimed exclusive $\sigma_8$ dependence is inherited from the mass function. A complementary falsifier is to apply the redshift-only stacking estimator to a large real galaxy redshift survey and test whether the recovered spin distribution shifts with $\sigma_8$ at the predicted rate.

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Extended reading notes

Core claim

The authors find that the probability density of void spins, $p(j)$, defined from the rescaled specific angular momentum of equal-mass point-like member halos, is well approximated by the generalized Gamma distribution $$p(j) = \frac{$j^{{k-1}}$}{2\Gamma(2k)\$\theta$^k}\exp\left[-\left(\frac{j}{\$\theta$}\right)^{1/2}\right]$$ for each of the 15 cosmologies, with deviations only in the lowest spin bin $j<1$. The best-fit parameters $\{k,\theta\}$ respond strongly and specifically to $\sigma_8$: changing $\sigma_8$ by about 10% from its fiducial value of $0.811$ produces a distance $D$ between best-fit parameter pairs of 3.4--4.4$\sigma$, whereas variations of $\Omega_{\rm cdm}h^2$ (0.108--0.132), $M_\nu$ (0--0.12 eV), and $w$ ($-1.1$ to $-0.9$) yield $D/\sigma_D$ values at or below 2.0. This exclusive $\sigma_8$-dependence is reported to be stable to changes in halo mass and number cuts. The conclusion is that the void spin distribution can act as a sensitive, nearly isolated constraint on $\sigma_8$, potentially breaking degeneracies that complicate other late-time probes.

Load-bearing premise

The load-bearing premise is that the spin distribution's sensitivity to $\sigma_8$ is not merely a reflection of the void halo mass function's own strong $\sigma_8$ dependence, since the paper has not yet separated the two effects.

Editorial extensions

If this is right

  • A 10% change in $\sigma_8$ shifts the generalized Gamma parameters by 3.4$\sigma$--4.4$\sigma$, implying that void spin distributions can discriminate between $\sigma_8$ values near the fiducial CMB value with high significance.
  • Varying $\Omega_{\rm cdm}h^2$, $M_\nu$, or $w$ over the tested ranges moves $\{k,\theta\}$ by less than 2$\sigma$, so a $\sigma_8$ constraint derived from void spins would be nearly orthogonal to these parameters.
  • The generalized Gamma form provides a compact parametric summary of void spin statistics across all 15 cosmologies, with the only systematic mismatch at $j<1$.
  • Redshift-only galaxy data can in principle recover projected void spins: stacking the residual redshifts and blueshifts of member galaxies around the projected spin direction yields a clear signal, strongest for voids with spin axes misaligned with the line of sight and high spin magnitudes.

Reading between the lines

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

  • Beyond the paper: if the exclusive $\sigma_8$ sensitivity persists under other void-finding algorithms and tracer populations, void spins could be combined with void abundance, shape, and weak-lensing void statistics in survey analyses to tighten $\sigma_8$ without the usual degeneracy with $M_\nu$.
  • Beyond the paper: the overlap with the halo mass function is the main threat to independence; the information-theoretic comparison the paper itself calls for would settle whether the spin distribution adds genuinely new $\sigma_8$ information over void halo abundance alone.
  • Beyond the paper: the redshift-only estimator is a kinematic measurement that could be tested immediately on existing spectroscopic surveys, but the required random optimization of projected spin axes has not yet been demonstrated on real data.
  • Beyond the paper: the fit failure at $j<1$ suggests low-spin voids are dominated by measurement noise; a version of the diagnostic that trims this regime might yield cleaner constraints, at the cost of discarding the most numerous voids.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper presents a numerical proof of concept that the probability density function of void spin magnitudes, p(j), measured from halo-defined cosmic voids, responds strongly and almost exclusively to the amplitude sigma_8, while being nearly insensitive to Omega_cdm h^2, total neutrino mass M_nu, and dark energy equation of state w. The authors identify voids with the Void-Finder algorithm in 15 AbacusSummit simulations that differ by one cosmological parameter at a time, measure void spins via Eq. (2.1), propose the generalized Gamma distribution of Eq. (3.1) as a fitting form, and quantify cosmological sensitivity through the distance D between best-fit parameter pairs (Table 3). The reported result is that ~10% variations in sigma_8 shift {k, theta} at about 4-sigma significance, whereas comparable variations in the other three parameters produce sub-2-sigma shifts for most models. The manuscript also contains a heuristic observational test based on redshift asymmetries of void member halos. The paper is transparent about several caveats, including an explicit statement in Section 5 that the connection between the sigma_8 effect on the void halo mass distribution and the claimed spin sensitivity has not yet been understood.

Significance. If the claimed exclusive sigma_8 dependence of void spins is confirmed to be intrinsic to the angular-momentum content of voids, the diagnostic would be a genuinely new late-time probe that could help break degeneracies in the sigma_8 tension. The paper has concrete strengths: it uses the public AbacusSummit simulations with controlled one-at-a-time parameter variations, applies a standard void finder, and quantifies sensitivity with a straightforward chi-square-based distance measure. The authors also make a useful first attempt at a redshift-only observational route to void spins. However, the central physical interpretation is currently unresolved: the measured spins are constructed from the positions and velocities of member halos whose selection depends on the sigma_8-sensitive halo mass function, and the paper explicitly leaves open how much of the signal is inherited from that selection. The current evidence is therefore suggestive rather than conclusive, and the claim of an independent, degeneracy-free sigma_8 probe requires an additional control analysis.

major comments (4)
  1. [Section 5, second caveat] The central claim of an "exclusive sigma_8-dependence" of the void spin distribution is not yet established because the spin measurement is defined through a sigma_8-dependent tracer population. The Void-Finder selection, the member-halo list, and the normalization velocity V_v in Eq. (2.1) all depend on the halo catalog with mass cut 10^11.5 h^-1 M_sun, and the halo mass function varies strongly with sigma_8 (Figure 7). The manuscript itself states in Section 5 that "it has yet to be understood how closely the sigma_8-effect on the void halo mass distribution is related to the sensitivity of the void spin distribution to sigma_8." Since the abstract and conclusions claim that the probe breaks degeneracies with Omega_cdm h^2, M_nu and w, this connection is load-bearing and must be addressed. A concrete test would be to re-weight the member halos so that the void halo mass distribution is matched across cosmologies, or to measure spins from uniformly selected mass bins, and then to verify that the D/sigma_D ranking in Table 3 survives. Alternatively, the authors could use mutual information to quantify how much information about sigma_8 remains in j after conditioning on the void halo mass function.
  2. [Section 3.3, robustness claim] The abstract and Section 3.3 state that the exclusive sigma_8 dependence is confirmed to be robust against variations of the halo mass and number cuts, but no quantitative results for those variations are shown anywhere in the paper. The sentence "Varying the values of halo number and mass cuts, we also repeat the analyses and confirm ..." is not accompanied by a figure, table, or numerical statement. This matters because Table 2 shows that the number of selected giant voids varies strongly across cosmologies (e.g., N_v(n_h >= 15) ranges from 153260 for c131 to 228304 for c134), so the stability of the best-fit parameters and of the D/sigma_D hierarchy under cut changes is not obvious. Please provide explicit results for at least two alternative cuts, or soften the abstract's robustness claim accordingly.
  3. [Section 3.1 and Table 3] The generalized Gamma fit is stated to fail in the lowest-j bin, j < 1, and the text later repeats "except for in the range of j <= 1". Because a chi-square fit over the full distribution gives large weight to bins where p(j) is largest, the low-j mismatch can in principle dominate the best-fit values of k and theta and thereby drive the D/sigma_D values in Table 3. The paper should test the robustness of the sigma_8 ranking by repeating the fit with the j < 1 region excluded, or by adding a model for the low-j behavior. If the D/sigma_D hierarchy changes materially, the current 4-sigma claim for data-model separation would need to be re-evaluated.
  4. [Table 3, significance interpretation] Each cosmology is represented by a single AbacusSummit realization, and the quoted errors in D/sigma_D are propagated from the internal fit errors of the best-fit parameters. The resulting significance therefore measures how well the two parameter estimates are separated relative to fitting noise under the assumed generalized-Gamma model; it does not include realization-to-realization cosmic variance. Given the very large void counts, the internal errors can be extremely small, which may inflate the formal significance. A brief statement acknowledging this limitation, or a comparison using multiple realizations available in AbacusSummit, would put the "~4-sigma" claim on firmer ground.
minor comments (4)
  1. [Table 3 caption] The phrase "non-Plank" should be "non-Planck" in the table caption.
  2. [Introduction] The sentence beginning "Although they have yet to blight the legacy of the concordance cosmology" is grammatically incomplete and should be revised.
  3. [Section 4] The feasibility test demonstrates stacked redshift asymmetries but does not actually reconstruct the projected spin distribution p(j_2d); the random optimization step needed to find the projected spin direction is explicitly left for future work. Please label the conclusion of this section as a heuristic consistency test rather than a full observational pipeline.
  4. [Section 5] There is a repeated word in the sentence "no such sensitive dependence of of {k, theta}"; please remove the second "of".

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the claimed sigma8-sensitivity is an empirical comparison across independent AbacusSummit simulations, and the self-citations only motivate method choices.

full rationale

The paper does not derive sigma8 from void spins; it computes void spin distributions p(j) directly from the halo catalogs of 15 fixed-cosmology simulations and quantifies how the best-fit parameters of the fitted generalized Gamma distribution (Eq. 3.1) shift when one cosmological parameter is varied. The distance metric D/sigma_D (Eq. 3.2 and Table 3) is a comparison of fitted parameter vectors, not a prediction whose input was fitted from the target result. The generalized Gamma form is an empirical model validated against the numerical p(j), so adopting it via the authors' earlier halo-spin work (Moon & Lee 2024) is not a circular reduction. The Section 5 admission that the relation between the sigma8 effect on the void halo mass function and the spin sensitivity 'has yet to be understood' is a real confound/independence limitation for the claim of a new probe, but it is not a circularity: no equation in the paper defines p(j) in terms of the mass function or forces the sigma8 dependence by construction. Self-citations (Lee & Park 2006 for void-spin definition and Void-Finder effectiveness; Moon & Lee 2024 for the Gamma ansatz; Lee et al. 2023 for error propagation) are method-motivational or routine and are not load-bearing for the central claim. Therefore no circular step is exhibited.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper's central claim rests on fitted parameters (k, theta) and several analysis choices (sc, nc, mass cut) that are not fully varied. The key physical assumption, that the spin signal is independent of the halo mass selection, is explicitly left unresolved in the discussion. No new physical entities are introduced.

free parameters (5)
  • generalized Gamma shape parameter k (per simulation) = 5.75 to 6.07 (Table 3, e.g., c000: 5.92)
    Fitted to each simulation's void spin distribution p(j) via chi-squared statistics; the paper's central claim is about how k varies with sigma8.
  • generalized Gamma scale parameter theta (per simulation) = 0.0295 to 0.0369 (Table 3, e.g., c000: 0.0329 in units of 10^2)
    Fitted together with k; its variation drives the claimed sigma8 sensitivity.
  • minimum void radius sc = 8 h^-1 Mpc
    Chosen by a statistical significance test (P>0.95) comparing voids to Poisson gaps; the paper does not test the robustness of the sigma8 sensitivity to this choice.
  • minimum halo number for voids nc = 15
    Chosen to ensure accurate spin measurements; paper claims robustness but does not show the variation.
  • halo mass cut = 10^11.5 h^-1 M_sun
    Halo mass threshold for selecting tracers; varies in absolute mass across simulations because h is set to match CMB acoustic scale, which could bias comparisons.
assumptions (5)
  • domain assumption Simulations accurately represent the nonlinear matter distribution for each cosmology (AbacusSummit N-body + COMPASO halos).
    The entire analysis rests on the fidelity of the simulations; the paper relies on the public AbacusSummit suite and its halo catalogs without independent verification.
  • domain assumption The Void-Finder algorithm with sc=8 h^-1 Mpc identifies genuine voids rather than Poisson gaps.
    The significance test in Section 2 establishes P>0.95 for sc>=8, but the algorithm choice itself is not varied.
  • ad hoc to paper The generalized Gamma distribution is an adequate universal fitting form for void spin distributions.
    The form is taken from Moon and Lee (2024) and is empirical; the paper notes it fails for j<1 and provides no physical derivation.
  • domain assumption Treating void member halos as equal-mass point-like particles does not bias the spin measurements.
    The spin definition (Eq. 2.1) drops the mass weighting used in the original Lee and Park (2006) definition because halo masses are hard to measure; this choice could affect the spin distribution shape.
  • domain assumption The one-parameter-at-a-time variations in the 15 simulations isolate the dependence on each parameter.
    The chosen simulations differ from Planck only in one parameter each, but h is not fixed; it is set to preserve the CMB acoustic scale, so particle mass resolution changes between models (mp varies), affecting the halo mass cut in physical units.

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Pith. "Pith review of Void spin distribution as a powerful probe of $\sigma_{8}$." pith.science (2026). https://pith.science/paper/4XFO7MJG

@misc{pith2026250109476,
  author       = {Pith},
  title        = {Pith review of: Void spin distribution as a powerful probe of $\sigma_8$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4XFO7MJG}},
  note         = {Machine review of arXiv:2501.09476}
}
abstract

We present a numerical proof of the concept that the void spin distributions can provide a tight constraint on the amplitude of matter density fluctuation on the scale of $8\,h^{-1}{\rm Mpc}$ ($\sigma_{8}$) without being severely deteriorated by the degeneracies of $\sigma_{8}$ with cold dark matter density parameter multiplied by the dimensionless Hubble parameter square ($\Omega_{\rm cdm}h^{2}$), total neutrino mass ($M_{\nu}$) and dark energy equation of state ($w$). Applying the Void-Finder algorithm~\cite{HV02} to a total of $15$ AbacusSummit $N$-body simulations of $15$ different cosmological models~\cite{summit1}, we identify the giant voids and measure the magnitudes of rescaled specific angular momenta of point-like void halos as their spins. The $15$ cosmologies include the Planck $\Lambda$CDM and $14$ non-Planck models, each of which differs among one another only in one of $\{\sigma_{8},\ \Omega_{\rm cdm}h^{2},\ M_{\nu},\ w\}$. We determine the probability density distribution of void spins for each model and for the first time find it to be well approximated by the generalized Gamma distribution with two characteristic parameters, $k$ and $\theta$. It turns out that the best-fit values of $k$ and $\theta$ exhibit very sensitive dependence only on $\sigma_{8}$, being almost insensitive to $\Omega_{\rm cdm}h^{2}$, $M_{\nu}$ and $w$. This exclusive $\sigma_{8}$-dependence of the void spin distributions is confirmed to be robust against the variation of the mass and number cuts of void halos. We also test an observational feasibility of estimating the void spins from real data on the galaxy redshifts.

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Works this paper leans on

81 extracted references · 19 canonical work pages

  1. [1]

    Hoyle and M

    F. Hoyle and M. S. Vogeley,Voids in the pscz survey and the updated zwicky catalog, Astrophys. J. 566 (2002) 641, doi:10.1086/338340 [arXiv:astro-ph/0109357 [astro-ph]]

    arXiv 2002

  2. [2]

    N. A. Maksimova, L. H. Garrison, D. J. Eisenstein, et al.,AbacusSummit: a massive set of high-accuracy, high-resolution N-body simulations, Mon. Not. Roy. Astron. Soc.508 (2021) 4037, doi:10.1093/mnras/stab2484 [arXiv:2110.11398 [astro-ph.CO]]

    arXiv 2021

  3. [3]

    Planck Collaboration, P. A. R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown, F. Atrio-Barandela, J. Aumont, C. Baccigalupi, A. J. Banday, et al.,Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys.571 (2014) A16, doi:10.1051/0004-6361/201321591, [arXiv:1303.5076 [astro-ph]]

    arXiv 2014

  4. [4]

    A. G. Riess, L. M. Macri, S. L. Hoffmann, D. Scolnic, S. Casertano, A. V. Filippenko, B. E. Tucker, M. J. Reid, D. O. Jones, J. M. Silverman, et al.,A 2.4% Determination of the Local Value of the Hubble Constant, Astrophys. J.826 (2016) 56, doi:10.3847/0004-637X/826/1/56, [arXiv:1604.01424 [astro-ph]]

    arXiv 2016

  5. [5]

    S. Alam, M. Aubert, S. Avila, C. Balland, J. E. Bautista, M. A. Bershady, D. Bizyaev, M. R. Blanton, A. S. Bolton, J. Bovy, et al.,Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory, Phys. Rev. D103 (2021) 083533, doi:10.1103/PhysRevD.103.0...

    arXiv 2021

  6. [6]

    Di Valentino, O

    E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, and J. Silk,In the realm of the Hubble tension-a review of solutions, Class. Quant. Grav. 38 (2021) 153001, doi:10.1088/1361-6382/ac086d, [arXiv:2103.01183 [astro-ph]]

    arXiv 2021

  7. [7]

    Joudaki, C

    S. Joudaki, C. Blake, C. Heymans, A. Choi, J. Harnois-Deraps, H. Hildebrandt, B. Joachimi, A. Johnson, A. Mead, D. Parkinson, et al.,CFHTLenS revisited: assessing concordance with Planck including astrophysical systematics, Mon. Not. Roy. Astron. Soc.465 (2017) 2033, doi:10.1093/mnras/stw2665, [arXiv:1601.05786 [astro-ph]]. – 21 –

    arXiv 2017

  8. [8]

    Hildebrandt, M

    H. Hildebrandt, M. Viola, C. Heymans, S. Joudaki, K. Kuijken, C. Blake, T. Erben, B. Joachimi, D. Klaes, L. Miller, et al.,KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing, Mon. Not. Roy. Astron. Soc.465 (2017) 1454, doi:10.1093/mnras/stw2805, [arXiv:1606.05338 [astro-ph]]

    arXiv 2017

Show all 81 references
  1. [9]

    Palanque-Delabrouille, C

    N. Palanque-Delabrouille, C. Yèche, N. Schöneberg, J. Lesgourgues, M. Walther, S. Chabanier, and E. Armengaud,Hints, neutrino bounds, and WDM constraints from SDSS DR14 Lyman-α and Planck full-survey data, JCAP 04 (2020) 038, doi:10.1088/1475-7516/2020/04/038, [arXiv:1911.0907...

    2020 arXiv

  2. [10]

    Asgari, T

    M. Asgari, T. Tröster, C. Heymans, H. Hildebrandt, J. L. van den Busch, A. H. Wright, A. Choi, T. Erben, B. Joachimi, S. Joudaki, et al.,KiDS+VIKING-450 and DES-Y1 combined: Mitigating baryon feedback uncertainty with COSEBIs, Astron. Astrophys.634 (2020) A127, doi:10.1051/000...

    2020 arXiv

  3. [11]

    Heymans, T

    C. Heymans, T. Tröster, M. Asgari, C. Blake, H. Hildebrandt, B. Joachimi, K. Kuijken, C.-A. Lin, A. G. Sánchez, J. L. van den Busch, et al.,KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints, Astron. Astrophys.646 (2021)...

    2021 arXiv

  4. [12]

    A. Amon, D. Gruen, M. A. Troxel, N. MacCrann, S. Dodelson, A. Choi, C. Doux, L. F. Secco, S. Samuroff, E. Krause, et al.,Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to data calibration, Phys. Rev. D105 (2022) 023514, doi:10.1103/PhysRevD.105.0...

    2022

  5. [13]

    X. Li, T. Zhang, S. Sugiyama, R. Dalal, R. Terasawa, M. M. Rau, R. Mandelbaum, M. Takada, S. More and M. A. Strauss,et al. Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions, Phys. Rev. D108 (2023) 123518, doi:10.1103/PhysRevD.108.123...

    2023 arXiv

  6. [14]

    Abdalla, G

    E. Abdalla, G. Franco Abellán, A. Aboubrahim, A. Agnello, O. Akarsu, Y. Akrami, G. Alestas, D. Aloni, L. Amendola and L. A. Anchordoqui,et al. Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and ano...

    2022 arXiv

  7. [15]

    Aghanimet al.[Planck], Planck 2018 results

    N. Aghanimet al.[Planck], Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6, doi:10.1051/0004-6361/201833910 [arXiv:1807.06209 [astro-ph.CO]]

    2020 arXiv

  8. [16]

    A. G. Riess, W. Yuan, L. M. Macri, D. Scolnic, D. Brout, S. Casertano, D. O. Jones, Y. Murakami, L. Breuval and T. G. Brink,et al. A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Te...

    2022 arXiv

  9. [17]

    Asgariet al.[KiDS], KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics, Astron

    M. Asgariet al.[KiDS], KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics, Astron. Astrophys.645 (2021) A104, doi:10.1051/0004-6361/202039070 [arXiv:2007.15633 [astro-ph.CO]]

    2021 arXiv

  10. [18]

    Shanks, L

    T. Shanks, L. Hogarth and N. Metcalfe,Gaia Cepheid parallaxes and ’Local Hole’ relieveH0 tension, Mon. Not. Roy. Astron. Soc.484 (2019) L64, doi:10.1093/mnrasl/sly239 [arXiv:1810.02595 [astro-ph.CO]]

    2019 arXiv

  11. [19]

    C. A. P. Bengaly, U. Andrade and J. S. Alcaniz,How does an incomplete sky coverage affect the Hubble Constant variance?, Eur. Phys. J. C79 (2019) 768, doi:10.1140/epjc/s10052-019-7284-4 [arXiv:1810.04966 [astro-ph.CO]]

    2019 arXiv

  12. [20]

    Mortsell, A

    E. Mortsell, A. Goobar, J. Johansson and S. Dhawan,Sensitivity of the Hubble Constant Determination to Cepheid Calibration, Astrophys. J.933 (2022) 212, doi:10.3847/1538-4357/ac756e [arXiv:2105.11461 [astro-ph.CO]]. – 22 –

    2022 arXiv

  13. [21]

    Blanchard, J

    A. Blanchard, J. Y. Héloret, S. Ilić, B. Lamine and I. Tutusaus,ΛCDM is alive and well, Open J. Astrophys. 7 (2024) 117170, doi:10.33232/001c.117170 [arXiv:2205.05017 [astro-ph.CO]]

    2024 arXiv

  14. [22]

    Dhawan, B

    S. Dhawan, B. Popovic, and A. Goobar,The axis of systematic bias in SN Ia cosmology and implications for DESI 2024 results, arXiv e-prints(2024) arXiv:2409.18668, doi:10.48550/arXiv.2409.18668, [arXiv:2409.18668 [astro-ph]]

    2024 doi arXiv

  15. [23]

    Efstathiou,Evolving Dark Energy or Supernovae Systematics?, [arXiv:2408.07175 [astro-ph.CO]]

    G. Efstathiou,Evolving Dark Energy or Supernovae Systematics?, [arXiv:2408.07175 [astro-ph.CO]]

    arXiv

  16. [24]

    Schöneberg, G

    N. Schöneberg, G. Franco Abellán, A. Pérez Sánchez, S. J. Witte, V. Poulin and J. Lesgourgues,The H0 Olympics: A fair ranking of proposed models, Phys. Rept.984 (2022) 1, doi:10.1016/j.physrep.2022.07.001 [arXiv:2107.10291 [astro-ph.CO]]

    2022 arXiv

  17. [25]

    A. R. Khalife, M. B. Zanjani, S. Galli, S. Günther, J. Lesgourgues and K. Benabed,Review of Hubble tension solutions with new SH0ES and SPT-3G data, JCAP 04 (2024) 059, doi:10.1088/1475-7516/2024/04/059 [arXiv:2312.09814 [astro-ph.CO]]

    2024 arXiv

  18. [26]

    A. G. Adameet al.[DESI], DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, [arXiv:2404.03002 [astro-ph.CO]]

    2024 arXiv

  19. [27]

    R. E. Keeley, S. Joudaki, M. Kaplinghat and D. Kirkby,Implications of a transition in the dark energy equation of state for theH0 and σ8 tensions, JCAP 12 (2019) 035, doi:10.1088/1475-7516/2019/12/035 [arXiv:1905.10198 [astro-ph.CO]]

    2019 arXiv

  20. [28]

    Jedamzik, L

    K. Jedamzik, L. Pogosian and G. B. Zhao,Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension, Commun. Phys.4 (2021) 123, doi:10.1038/s42005-021-00628-x [arXiv:2010.04158 [astro-ph.CO]]

    2021 arXiv

  21. [29]

    Sakr,Extensions to ΛCDM at Intermediate Redshifts to Solve the Tensions?, PoS CORFU2022 (2023) 262, doi:10.22323/1.436.0262 [arXiv:2305.02913 [astro-ph.CO]]

    Z. Sakr,Extensions to ΛCDM at Intermediate Redshifts to Solve the Tensions?, PoS CORFU2022 (2023) 262, doi:10.22323/1.436.0262 [arXiv:2305.02913 [astro-ph.CO]]

    2023 arXiv

  22. [30]

    Akarsu, E

    Ö. Akarsu, E. Ó. Colgáin, A. A. Sen and M. M. Sheikh-Jabbari,ΛCDM Tensions: Localising Missing Physics through Consistency Checks, Universe 10 (2024) 305, doi:10.3390/universe10080305 [arXiv:2402.04767 [astro-ph.CO]]

    2024 arXiv

  23. [31]

    S. J. Clark, K. Vattis, J. Fan and S. M. Koushiappas,H0 and S8 tensions necessitate early and late time changes toΛCDM, Phys. Rev. D107 (2023) 083527, doi:10.1103/PhysRevD.107.083527 [arXiv:2110.09562 [astro-ph.CO]]

    2023 arXiv

  24. [32]

    Heisenberg, H

    L. Heisenberg, H. Villarrubia-Rojo and J. Zosso,Simultaneously solving the H0 andσ8 tensions with late dark energy, Phys. Dark Univ.39 (2023) 101163, doi:10.1016/j.dark.2022.101163 [arXiv:2201.11623 [astro-ph.CO]]

    2023

  25. [33]

    S. Vagnozzi,Seven Hints That Early-Time New Physics Alone Is Not Sufficient to Solve the Hubble Tension, Universe 9 (2023) 393, doi:10.3390/universe9090393, [arXiv:2308.16628 [astro-ph]]

    2023 arXiv

  26. [34]

    V. R. Eke, S. Cole and C. S. Frenk,Using the evolution of clusters to constrain Omega, Mon. Not. Roy. Astron. Soc.282 (1996), 263-280 doi:10.1093/mnras/282.1.263 [arXiv:astro-ph/9601088 [astro-ph]]

    1996 arXiv

  27. [35]

    L. M. Wang and P. J. Steinhardt,Cluster abundance constraints on quintessence models, Astrophys. J. 508 (1998) 483, doi:10.1086/306436 [arXiv:astro-ph/9804015 [astro-ph]]

    1998 arXiv

  28. [36]

    Lesgourgues and S

    J. Lesgourgues and S. Pastor,Massive neutrinos and cosmology, Phys. Rept.429 (2006) 307, doi:10.1016/j.physrep.2006.04.001 [arXiv:astro-ph/0603494 [astro-ph]]

    2006 arXiv

  29. [37]

    J. P. Henry, A. E. Evrard, H. Hoekstra, A. Babul and A. Mahdavi,The X-ray Cluster Normalization of the Matter Power Spectrum, Astrophys. J.691 (2009) 1307, doi:10.1088/0004-637X/691/2/1307 [arXiv:0809.3832 [astro-ph]]. – 23 –

    2009 arXiv

  30. [38]

    Moresco, L

    M. Moresco, L. Amati, L. Amendola, S. Birrer, J. P. Blakeslee, M. Cantiello, A. Cimatti, J. Darling, M. Della Valle and M. Fishbach,et al. Unveiling the Universe with emerging cosmological probes, Living Rev. Rel.25 (2022) 6, doi:10.1007/s41114-022-00040-z [arXiv:2201.07241 [a...

    2022 arXiv

  31. [39]

    Krauseet al., A Parameter-Masked Mock Data Challenge for Beyond-Two-Point Galaxy Clustering Statistics, [arXiv:2405.02252 [astro-ph.CO]]

    E. Krauseet al., A Parameter-Masked Mock Data Challenge for Beyond-Two-Point Galaxy Clustering Statistics, [arXiv:2405.02252 [astro-ph.CO]]

    arXiv

  32. [40]

    Lee and D

    J. Lee and D. Park,Constraining Dark Energy Equation of State with Cosmic Voids, Astrophys. J. Lett.696 (2009) L10, doi:10.1088/0004-637X/696/1/L10 [arXiv:0704.0881 [astro-ph]]

    2009 arXiv

  33. [41]

    Biswas, E

    R. Biswas, E. Alizadeh and B. D. Wandelt,Voids as a precision probe of dark energy, Phys. Rev. D 82 (2010) 023002, doi:10.1103/PhysRevD.82.023002 [arXiv:1002.0014 [astro-ph.CO]]

    2010 arXiv

  34. [42]

    E. G. P. Bos, R. van de Weygaert, K. Dolag and V. Pettorino,The darkness that shaped the void: dark energy and cosmic voids, Mon. Not. Roy. Astron. Soc.426 (2012) 440, doi:10.1111/j.1365-2966.2012.21478.x [arXiv:1205.4238 [astro-ph.CO]]

    2012

  35. [43]

    Lavaux and B

    G. Lavaux and B. D. Wandelt,Precision Cosmography with Stacked Voids, Astrophys. J.754 (2012) 109, doi:10.1088/0004-637X/754/2/109 [arXiv:1110.0345 [astro-ph.CO]]

    2012 arXiv

  36. [44]

    Massara, F

    E. Massara, F. Villaescusa-Navarro, M. Viel and P. M. Sutter,Voids in massive neutrino cosmologies, JCAP 11 (2015) 018, doi:10.1088/1475-7516/2015/11/018 [arXiv:1506.03088 [astro-ph.CO]]

    2015 arXiv

  37. [45]

    Novosyadlyj and M

    B. Novosyadlyj and M. Tsizh,Voids in the Cosmic Web as a probe of dark energy, Condensed Matter Phys. 20 (2017) 13901, doi:10.5488/CMP.20.13901 [arXiv:1703.00364 [astro-ph.CO]]

    2017 arXiv

  38. [46]

    Verza, A

    G. Verza, A. Pisani, C. Carbone, N. Hamaus and L. Guzzo,The Void Size Function in Dynamical Dark Energy Cosmologies, JCAP 12 (2019) 040, doi:10.1088/1475-7516/2019/12/040 [arXiv:1906.00409 [astro-ph.CO]]

    2019 arXiv

  39. [47]

    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, JCAP 12 (2020) 023, doi:10.1088/1475-7516/2020/12/023 [arXiv:2007.07895 [astro-ph.CO]]

    2020 arXiv

  40. [48]

    Rezaei,Dark Matter-Dark Energy Interaction and the Shape of Cosmic Voids, Astrophys

    Z. Rezaei,Dark Matter-Dark Energy Interaction and the Shape of Cosmic Voids, Astrophys. J. 902 (2020) 102, doi:10.3847/1538-4357/abb59d [arXiv:2010.10823 [astro-ph.CO]]

    2020

  41. [49]

    C. T. Davies, M. Cautun, B. Giblin, B. Li, J. Harnois-Déraps and Y. C. Cai,Constraining cosmology with weak lensing voids, Mon. Not. Roy. Astron. Soc.507 (2021) 2267, doi:10.1093/mnras/stab2251 [arXiv:2010.11954 [astro-ph.CO]]

    2021

  42. [50]

    Contariniet al.[Euclid], Euclid: Cosmological forecasts from the void size function, Astron

    S. Contariniet al.[Euclid], Euclid: Cosmological forecasts from the void size function, Astron. Astrophys. 667 (2022) A162, doi:10.1051/0004-6361/202244095 [arXiv:2205.11525 [astro-ph.CO]]

    2022 arXiv

  43. [51]

    Verza, C

    G. Verza, C. Carbone, A. Pisani and A. Renzi,DEMNUni: disentangling dark energy from massive neutrinos with the void size function, JCAP 12 (2023) 044, doi:10.1088/1475-7516/2023/12/044 [arXiv:2212.09740 [astro-ph.CO]]

    2023 arXiv

  44. [52]

    Ebrahimi,Phenomenological emergent dark energy versus theΛCDM: ellipticity of cosmic voids, Mon

    E. Ebrahimi,Phenomenological emergent dark energy versus theΛCDM: ellipticity of cosmic voids, Mon. Not. Roy. Astron. Soc.527 (2024) 11962, doi:10.1093/mnras/stad3627

    2024 doi

  45. [53]

    Park and J

    D. Park and J. Lee,The Void Ellipticity Distribution as a Probe of Cosmology, Phys. Rev. Lett. 98 (2007) 081301, doi:10.1103/PhysRevLett.98.081301 [arXiv:astro-ph/0610520 [astro-ph]]

    2007 arXiv

  46. [54]

    Fernández-García, J

    E. Fernández-García, J. E. Betancort-Rijo, F. Prada, T. Ishiyama and A. Klypin,Constraining cosmological parameters using void statistics from the SDSS survey, [arXiv:2406.13736 [astro-ph.CO]]. – 24 –

    arXiv

  47. [55]

    Lee and D

    J. Lee and D. Park,Rotation of Cosmic Voids and Void-Spin Statistics, Astrophys. J.652 (2006) 1, doi:10.1086/507936 [arXiv:astro-ph/0606477 [astro-ph]]

    2006 arXiv

  48. [56]

    L. H. Garrison, D. J. Eisenstein, D. Ferrer, N. A. Maksimova and P. A. Pinto,The abacus cosmological N-body code, Mon. Not. Roy. Astron. Soc.508 (2021) 575, doi:10.1093/mnras/stab2482 [arXiv:2110.11392 [astro-ph.CO]]

    2021 arXiv

  49. [57]

    M. V. L. Metchnik,A fast N-body scheme for computational cosmology, Ph.D. Thesis. U. of Arizona (2009)

    2009

  50. [58]

    Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview(2011) arXiv e-prints

    J. Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview(2011) arXiv e-prints. doi:10.48550/arXiv.1104.2932

    2011 doi arXiv

  51. [59]

    L. H. Garrison, D. J. Eisenstein, D. Ferrer, et al.,AbacusSummit: Initial results from a suite of massive N-body simulations, Mon. Not. Roy. Astron. Soc.508 (2021) 575, doi:10.1093/mnras/stab2482 [arXiv:2110.11397 [astro-ph.CO]]

    2021 arXiv

  52. [60]

    Hadzhiyska, D

    B. Hadzhiyska, D. Eisenstein, S. Bose, L. H. Garrison and N. Maksimova,compaso: A new halo finder for competitive assignment to spherical overdensities, Mon. Not. Roy. Astron. Soc.509 (2021) 501, doi:10.1093/mnras/stab2980 [arXiv:2110.11408 [astro-ph.CO]]

    2021 arXiv

  53. [61]

    Hadzhiyska, D

    B. Hadzhiyska, D. J. Eisenstein, S. Bose, et al.,Halo occupation distribution modeling in AbacusSummit simulations, Mon. Not. Roy. Astron. Soc.509 (2022) 501, doi:10.1093/mnras/stab2980 [arXiv:2110.11399 [astro-ph.CO]]

    2022 arXiv

  54. [62]

    M. S. Warren, P. J. Quinn, J. K. Salmon, W. H. Zurek,Dark Halos Formed via Dissipationless Collapse. I. Shapes and Alignment of Angular Momentum., Astrophys. J.399 (1992) 405, doi:10.1086/171937

    1992 doi

  55. [63]

    El-Ad and T

    H. El-Ad and T. Piran,Voids in the large scale structure, Astrophys. J.491 (1997) 421, doi:10.1086/304973 [arXiv:astro-ph/9702135 [astro-ph]]

    1997 arXiv

  56. [64]

    M. C. Cousinou, A. Pisani, A. Tilquin, N. Hamaus, A. J. Hawken, and S. Escoffier, Multivariate analysis of cosmic void characteristics, Astron. Comput.27 (2019) 53, doi:10.1016/j.ascom.2019.03.001, [arXiv:1805.07181 [astro-ph]]

    2019 arXiv

  57. [65]

    Hamaus, M

    N. Hamaus, M. Aubert, A. Pisani, S. Contarini, G. Verza, M. C. Cousinou, S. Escoffier, A. Hawken, G. Lavaux, G. Pollina, et al.,Euclid: Forecasts from redshift-space distortions and the Alcock-Paczynski test with cosmic voids, Astron. Astrophys.658 (2022) A20, doi:10.1051/0004...

    2022 arXiv

  58. [66]

    Verza, G

    G. Verza, G. Degni, A. Pisani, N. Hamaus, E. Massara, A. Benson, S. Escoffier, Y. Wang, Z. Zhai, O. Doré, et al.,Cosmology with voids from the Nancy Grace Roman Space Telescope, arXiv e-prints (2024) arXiv:2410.19713, doi:10.48550/arXiv.2410.19713, [arXiv:2410.19713 [astro-ph]]

    2024 doi

  59. [67]

    Banerjee and N

    A. Banerjee and N. Dalal,Simulating nonlinear cosmological structure formation with massive neutrinos, JCAP 11 (2016) 015, doi:10.1088/1475-7516/2016/11/015, [arXiv:1606.06167 [astro-ph]]

    2016 arXiv

  60. [68]

    N. D. Padilla, L. Ceccarelli, and D. G. Lambas,Spatial and dynamical properties of voids in a ΛCDM universe, Mon. Not. Roy. Astron. Soc.363 (2005) 977, doi:10.1111/j.1365-2966.2005.09500.x, [arXiv:astro-ph/0508297 [astro-ph]]

    2005

  61. [69]

    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, doi:10.1093/mnras/stv019, [arXiv:1501.02120 [astro-ph]]

    2015 arXiv

  62. [70]

    D. J. Paz, C. M. Correa, S. R. Gualpa, A. N. Ruiz, C. S. Bederián, R. D. Graña, and N. D. Padilla,Guess the cheese flavour by the size of its holes: a cosmological test using the abundance of popcorn voids, Mon. Not. Roy. Astron. Soc.522 (2023) 2553, doi:10.1093/mnras/stad1146...

    2023 arXiv

  63. [71]

    M. C. Neyrinck,ZOBOV: a parameter-free void-finding algorithm, Mon. Not. Roy. Astron. Soc. 386 (2008) 2101, doi:10.1111/j.1365-2966.2008.13180.x, [arXiv:0712.3049 [astro-ph]]

    2008

  64. [72]

    P. M. Sutter, G. Lavaux, N. Hamaus, A. Pisani, B. D. Wandelt, M. Warren, F. Villaescusa-Navarro, P. Zivick, Q. Mao, B. B. Thompson, et al.,VIDE: The Void Identification and Examination toolkit, Astron. Comput.9 (2015) 1, doi:10.1016/j.ascom.2014.10.002, [arXiv:1406.1191 [astro-ph]]

    2015 arXiv

  65. [73]

    Nadathur, P

    S. Nadathur, P. M. Carter, W. J. Percival, H. A. Winther, and J. E. Bautista,REVOLVER: REal-space VOid Locations from suVEy Reconstruction, Astrophysics Source Code Library (2019) ascl:1907.023

    2019

  66. [74]

    Lee and J

    J. Lee and J. S. Moon,An Observed Transition of Galaxy Spins on Void Surfaces, Astrophys. J. Lett. 951 (2023) L26, doi:10.3847/2041-8213/acdd75 [arXiv:2305.04409 [astro-ph.CO]]

    2023 arXiv

  67. [75]

    J. S. Bullock, A. Dekel, T. S. Kolatt, A. V. Kravtsov, A. A. Klypin, C. Porciani and J. R. Primack,A Universal angular momentum profile for galactic halos, Astrophys. J.555 (2001) 240, doi:10.1086/321477 [arXiv:astro-ph/0011001 [astro-ph]]

    2001 arXiv

  68. [76]

    J. S. Moon and J. Lee,Mutual information between galaxy properties and the initial predisposition, JCAP 05 (2024) 111, doi:10.1088/1475-7516/2024/05/111 [arXiv:2311.03632 [astro-ph.CO]]

    2024 arXiv

  69. [77]

    J. Lee, S. Ryu and M. Baldi,Disentangling Modified Gravity and Massive Neutrinos with Intrinsic Shape Alignments of Massive Halos, Astrophys. J.945 (2023) 15, doi:10.3847/1538-4357/acabbc [arXiv:2206.03406 [astro-ph.CO]]

    2023 arXiv

  70. [78]

    P. Wang, N. I. Libeskind, E. Tempel, X. Kang and Q. Guo,Possible observational evidence for cosmic filament spin, Nature Astron.5 (2021) 839, doi:10.1038/s41550-021-01380-6 [arXiv:2106.05989 [astro-ph.GA]]

    2021 arXiv

  71. [79]

    Shandarin, H

    S. Shandarin, H. A. Feldman, K. Heitmann and S. Habib,Shapes and sizes of voids in the lambda-cdm universe: excursion set approach, Mon. Not. Roy. Astron. Soc.367 (2006) 1629, doi:10.1111/j.1365-2966.2006.10062.x [arXiv:astro-ph/0509858 [astro-ph]]

    2006

  72. [80]

    J. R. Bond, L. Kofman and D. Pogosyan,How filaments are woven into the cosmic web, Nature 380 (1996) 603, doi:10.1038/380603a0 [arXiv:astro-ph/9512141 [astro-ph]]

    1996 arXiv

  73. [81]

    Shannon,A Mathematical Theory of Communication, The Bell Sys

    C. Shannon,A Mathematical Theory of Communication, The Bell Sys. Tech. J.27 (1948) 379, doi:10.1002/j.1538-7305.1948.tb01338.x – 26 –

    1948

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