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REVIEW 3 major objections 4 minor 60 references

The first simulation pipeline that runs from deep inflation to today shows axion-U(1) inflation leaves a measurable boost in early massive halos.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · deepseek-v4-flash

2026-08-03 00:21 UTC pith:YJ5IAIZN

load-bearing objection A genuinely new inflation-to-N-body pipeline with suggestive halo mass function predictions, but the headline numbers need a few missing details (halo finder, error bars, cross-correlation check) before they should be taken as conclusive. the 3 major comments →

arxiv 2607.28800 v1 pith:YJ5IAIZN submitted 2026-07-30 astro-ph.CO gr-qc

Ab Initio Cosmological Simulations: From Inflation to Present-Day Structure Formation

Drew Jamieson , Angelo Caravano , Eiichiro Komatsu This is my paper
classification astro-ph.CO gr-qc PACS 98.80.Cq
keywords inflationprimordial non-Gaussianityab initio simulationN-body simulationaxion-U(1) inflationhalo mass functionmatter power spectrum21-cm cosmology
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper establishes a new way to predict the cosmic web: instead of assuming Gaussian or template-based initial conditions, it simulates the nonlinear dynamics of inflation on a lattice, converts the resulting curvature field into the linear matter density, and evolves it with an N-body simulation to z=0. Applied to axion-U(1) inflation, the pipeline predicts that gauge-field-sourced fluctuations produce a blue-tilted power spectrum and a full hierarchy of non-Gaussian correlations. These make small-scale structure at high redshift much more abundant: at z=12, halo counts are more than 200% higher than in single-field inflation, and still 60% higher than Gaussian simulations with the same power spectrum, isolating a genuine non-Gaussianity effect. The paper argues that this makes high-redshift 21-cm, line-intensity, and galaxy surveys direct probes of inflationary physics.

Core claim

The central discovery is a field-level prediction that bypasses standard template-based parametrizations of primordial non-Gaussianity. By isolating the vacuum and sourced components of the curvature perturbation via paired lattice simulations of inflation, and mapping the curvature field to linear matter density through the standard transfer function, the authors find that the sourced axion-gauge fluctuations survive to late times. They enhance matter power by about 10% at k=1 h/Mpc (z≥2) and about 40% at k=10 h/Mpc (z≥8), and boost the halo mass function far more strongly, especially for the most massive halos at z=12. The excess over power-matched Gaussian simulations (60%) demonstrates t

What carries the argument

The core mechanism is the decomposition of the primordial curvature perturbation into an uncorrelated sum ζ = ζ_vac + ζ_src, obtained by running paired lattice simulations of inflation with identical seeds and the axion-gauge coupling switched off in one. ζ_src carries a blue-tilted, scale-dependent, non-separable hierarchy of higher-order correlations produced by the Chern-Simons interaction between the axion and the U(1) gauge field. These curvature fields are converted to linear matter density perturbations through the standard transfer function and growth factor, then used as third-order Lagrangian perturbation theory initial conditions for N-body evolution. The signature in the halo mas

Load-bearing premise

The sourced curvature perturbation is an adiabatic scalar mode uncorrelated with the vacuum mode, so it can be linearly mapped to late-time matter through the standard transfer function; if that mapping fails, the halo-mass-function prediction loses its foundation.

What would settle it

Search for the predicted 40% enhancement of matter power at k≈10 h/Mpc or the 200% halo-count excess at z≈12 in 21-cm or high-redshift galaxy surveys; if the observed structure on these scales matches Gaussian initial conditions with the same power spectrum, the axion-U(1) prediction is ruled out.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • High-redshift observations (21-cm, line-intensity mapping, galaxy surveys at z~6-12) should see a scale-dependent excess of small-scale power and an overabundance of massive halos relative to ΛCDM with Gaussian initial conditions.
  • The 60% excess over power-matched Gaussian simulations shows that primordial non-Gaussianity alone can be constrained from the halo mass function nearly independently of the power spectrum.
  • The enhancement grows with halo mass, so the rarest, most massive high-redshift halos are the most sensitive test of this class of models.
  • Nonlinear gravitational clustering erases much of the signal by z=0, so low-redshift surveys will see little; the cleanest constraints come from quasilinear scales at high redshift.
  • The log-Edgeworth prediction from the measured cumulants reproduces the N-body halo counts, enabling fast analytic forecasts from lattice-generated primordial fields.

Where Pith is reading between the lines

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

  • The same pipeline could be applied to other nonlinear inflationary or reheating models, turning any lattice-simulable early-universe field into a halo-level prediction without template assumptions.
  • The non-separable, blue-tilted bispectrum shape implies template-based primordial non-Gaussianity searches (local/equilateral/orthogonal) may miss the signal; simulation-calibrated estimators would be needed.
  • If confirmed, the predicted high-redshift halo excess would offer an alternative explanation for the abundance of massive galaxies at early times, independent of astrophysical efficiency arguments.
  • A testable extension would be to split the sourced field into bispectrum-only and trispectrum-only parts (e.g., by setting higher cumulants to zero) to quantify which statistic drives the halo boost; the paper's observed hierarchy suggests the bispectrum dominates at low mass and the trispectrum contributes at high mass.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper presents a new ab initio pipeline that connects lattice simulations of axion-U(1) inflation to cosmological N-body simulations: ALEF generates 3D curvature perturbations from nonlinear inflationary dynamics; the resulting field is converted to linear matter density with CLASS and used to set 3LPT initial conditions at z=15 for gadget-4. Three initial-condition sets are compared: AU1 (full axion-U(1)), SF (single-field with g_CS=0), and G (Gaussian with power spectrum matched to AU1). The authors report enhanced small-scale matter power and, more importantly, halo mass function enhancements of >200% at z=12 relative to SF and 60% relative to G, interpreting the residual after power matching as the effect of primordial non-Gaussianity. The Loverde-Smith/Tinker log-Edgeworth prediction is compared with the N-body halo mass function and claimed to be in good agreement.

Significance. If the result holds, this is a genuinely novel methodological advance: it replaces template-based primordial non-Gaussianity with field-level predictions from nonlinear inflationary dynamics, and it yields falsifiable predictions for high-redshift surveys, 21-cm, and line-intensity mapping. The paper's strengths include paired seed-matched control simulations (SF and G), Planck-calibrated background and potential parameters, use of public simulation codes, and direct measurement of primordial bispectrum/trispectrum. The main caveats are that the central halo mass function claim lacks a halo finder/mass definition and error bars, and that the uncorrelated vacuum/sourced decomposition is asserted but not numerically demonstrated. These are fixable with additional analysis and reporting.

major comments (3)
  1. [§V.B, Fig. 2] The central quantitative claim is not reproducible as stated. No halo finder (FoF linking length, SO overdensity) or mass definition (M200b, M200c, Mvir) is given, and the lower panels of Fig. 2 show nAU1/nSF−1 and nAU1/nG−1 without any error bars. Since ten realizations exist, realization scatter can be estimated directly and should be shown. In addition, the statement that the Loverde-Smith/Tinker dashed curves are in 'good agreement' is unsupported without a residual or goodness-of-fit statistic. Please state the finder and mass definition, add error bars, and quantify the agreement.
  2. [§V.B, Table I] For the z=12 small-box results, the plotted mass range (Fig. 2, right panels, M ~1e10–1e11 M_sun) corresponds to halos of roughly 100–1,400 particles for a 4×512^3 run in a 100 Mpc box (particle mass ~7×10^7 M_sun). No minimum halo particle number or resolution/convergence test is reported. The 200% enhancement may therefore be affected by shot noise and mass-assignment systematics, especially at the lowest masses. Please report the particle mass, the minimum virial particle threshold, and a convergence test (e.g., comparing with a higher-resolution run or varying the minimum particle threshold).
  3. [§IV and App. B] The decomposition ζ=ζ_vac+ζ_src relies on the assertion that the cross-correlation between ζ_vac and ζ_src is 'negligibly small,' but no numerical evidence is shown. The paired seed-matched ALEF simulations make the cross spectrum directly measurable: report ⟨ζ_SF (ζ_AU1−ζ_SF)⟩ or the cross power spectrum, normalized to P_vac and P_src, over the k-range used to construct the N-body initial conditions. If this cross term is non-negligible, the source-term isolation and the interpretation of the AU1−G comparison as isolating primordial non-Gaussianity would need to be revisited.
minor comments (4)
  1. [§IV, Table I] 'Three sets of ten simulations with the same random seed but different initial conditions' is ambiguous: does each of the ten realizations share the same seed across AU1/SF/G, or are the ten realizations independent? Please clarify.
  2. [Abstract] There is a missing space in 'Thisab initioapproach' in the abstract; also, 'the entire history of the universe' should be qualified, since the N-body evolution starts at z=15 rather than at the end of inflation.
  3. [§V.A] The quoted 2% and 10% PNG effects in the matter power spectrum are given without uncertainties. With ten realizations, error bars should be reported in the text or figure.
  4. [App. B, Fig. 4] The parity-odd trispectrum is stated to be 'negligibly small' but no numerical bound or plot is shown; please state the suppression factor relative to the parity-even part.

Circularity Check

0 steps flagged

No significant circularity: forward ab initio pipeline with externally fixed parameters and controlled comparisons.

full rationale

The paper's central claim is a forward modeling result, not a reduction of outputs to inputs. The model parameters g_CS and M_phi are fixed by Planck 2018 constraints (Sec. IV), not by the halo mass function. The N-body simulations are outputs of an independent pipeline (ALEF -> transfer function -> Music2/MonofonIC -> Gadget-4). The AU1/SF/G comparison is a controlled experiment: G is constructed by rescaling the Gaussian vacuum component to match the AU1 power spectrum, so the AU1-G difference isolates non-Gaussian effects rather than being fitted to them. The LoVerde-Smith/Tinker comparison is a post-hoc consistency check using cumulants measured from the initial conditions; the halo mass function is not used to determine those cumulants. The main self-reference is the ALEF paper [35], which is a separately published numerical code with its own convergence tests; it is used as a tool, not as an unverified uniqueness theorem or as the source of the central prediction. The Appendix B assumption that zeta_vac and zeta_src are negligibly correlated is a physical assumption that could be checked and is a correctness risk rather than a circular step, because the matched-power G control defines non-Gaussianity at fixed power regardless of the cross-correlation value. No specific equation or fitted parameter reduces to the predicted halo mass function, so no concrete circular reduction can be exhibited; the paper is self-contained against external benchmarks and merits a low score.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 0 invented entities

Model parameters are taken from Planck 2018 and the g_CS coupling is saturated to the Planck bispectrum bound, so the 'ab initio' prediction is conditioned on standard ΛCDM and an extreme allowed coupling. The core physical assumptions are the conservation of ζ on superhorizon scales, the adiabaticity of the sourced perturbations, and uncorrelated vacuum-sourced fields. No new physical entities are introduced.

free parameters (3)
  • g_CS (Chern-Simons coupling) = 750 M_Pl^-1
    Chosen to saturate the Planck 2018 2σ upper bound on the equilateral bispectrum (Sec. IV); not derived, and it maximizes the sourced signal.
  • M_ϕ (inflaton mass scale in α-attractor potential) = 4.653e-6 M_Pl
    Fixed so the vacuum power spectrum matches Planck 2018 A_s (Sec. IV).
  • α_V (α-attractor potential parameter) = sqrt(20/3)
    Model choice fixing the vacuum spectral tilt/tensor ratio to match Planck (Sec. IV).
axioms (7)
  • standard math Curvature perturbations ζ are conserved on superhorizon scales through reheating (Weinberg theorem).
    Section IV; standard result used to justify mapping ζ at end of inflation to late-time matter perturbations.
  • domain assumption Sourced perturbations ζ_src are adiabatic scalar curvature perturbations and can be mapped with the same linear transfer function as vacuum modes.
    Section IV; the gauge field vector modes decay but sourced inflaton fluctuations are treated as standard adiabatic curvature.
  • domain assumption ζ_vac and ζ_src are uncorrelated, so ζ_src = ζ_AU1 - ζ_SF isolates sourcing.
    Appendix B; relies on weak backreaction; if false, isolation of PNG is invalid.
  • domain assumption ALEF lattice simulations correctly capture nonlinear axion-U(1) dynamics (convergence claimed in Ref. [35]).
    Section II; no convergence data shown in this paper.
  • domain assumption Bunch-Davies vacuum initial conditions for lattice fields.
    Section II; standard but assumed for the model.
  • domain assumption Log-Edgeworth/Tinker mass function applies to these strongly non-Gaussian, blue-tilted fields.
    Section V.B; used for comparison, not for central claim.
  • domain assumption Weak backreaction regime only; strong backreaction is not relevant to the simulated predictions.
    Section III; the simulation excludes strong backreaction where decomposition fails.

pith-pipeline@v1.3.0-alltime-deepseek · 12994 in / 18612 out tokens · 174794 ms · 2026-08-03T00:21:10.808767+00:00 · methodology

0 comments
read the original abstract

The cosmic web preserves a record of the physics that shaped the universe in its earliest moments, the period of exponential expansion known as cosmic inflation. However, if inflation involves significant nonlinear interactions, there are no direct theoretical predictions for the resulting cosmic web. We present the first simulation of the entire history of the universe, from deep in the inflationary epoch to the present-day cosmic structure. Applying this to axion-U(1) inflation, we find that early-universe interactions enhance small-scale structure at high redshift, imprinting the matter power spectrum and the mass function of dark matter halos with signatures of a modified primordial curvature power spectrum and non-Gaussianity. These signatures make high-redshift galaxy surveys, 21-cm observations, and line-intensity mapping promising probes of inflationary physics. More broadly, this ab initio approach provides a novel framework for mapping the signatures of nonlinear inflationary dynamics onto observable cosmic structures across cosmic time.

Figures

Figures reproduced from arXiv: 2607.28800 by Angelo Caravano, Drew Jamieson, Eiichiro Komatsu.

Figure 1
Figure 1. Figure 1: FIG. 1. Field-level view of our simulation pipeline. The [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Matter power spectra (left) and halo mass functions (right) from [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Slices of the nonlinear density field from [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Left [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

60 extracted references · 39 linked inside Pith

  1. [1]

    G” (Gaussian), “SF

    The magnetic and electric fields are defined as ⃗B= ⃗∇ ×⃗Aand ⃗E=− ⃗A′ − ⃗∇φ, respectively, andg CS is the Chern-Simons coupling strength.V ,ϕ is the slope of the inflaton potential andδϕ=ϕ− ¯ϕ. The wave operator is□f=−f ′′ +∇ 2f, with primes denoting derivatives with respect to conformal timeτ. The scale factorahas 3 a conformal Hubble rateH=a ′/a=aHand ...

    2094

  2. [2]

    Baumann,Cosmology(Cambridge University Press, 2022)

    D. Baumann,Cosmology(Cambridge University Press, 2022)

    2022

  3. [3]

    D. N. Spergelet al.(WMAP), Astrophys. J. Suppl.148, 175 (2003), arXiv:astro-ph/0302209

    Pith/arXiv arXiv 2003

  4. [4]

    Tegmarket al.(SDSS), Phys

    M. Tegmarket al.(SDSS), Phys. Rev. D69, 103501 (2004), arXiv:astro-ph/0310723

    Pith/arXiv arXiv 2004

  5. [5]

    Aghanimet al.(Planck), Astron

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  6. [6]

    A. A. Starobinsky, Phys. Lett. B91, 99 (1980)

    1980

  7. [7]

    A. H. Guth, Phys. Rev. D23, 347 (1981)

    1981

  8. [8]

    Sato, Mon

    K. Sato, Mon. Not. Roy. Astron. Soc.195, 467 (1981)

    1981

  9. [9]

    Albrecht and P

    A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett.48, 1220 (1982)

    1982

  10. [10]

    A. D. Linde, Phys. Lett. B108, 389 (1982)

    1982

  11. [11]

    V. F. Mukhanov and G. V. Chibisov, JETP Lett.33, 532 (1981), [Pisma Zh. Eksp. Teor. Fiz.33,549(1981)]

    1981

  12. [12]

    S. W. Hawking, Phys. Lett.115B, 295 (1982)

    1982

  13. [13]

    A. A. Starobinsky, Phys. Lett.117B, 175 (1982)

    1982

  14. [14]

    A. H. Guth and S. Y. Pi, Phys. Rev. Lett.49, 1110 (1982)

    1982

  15. [15]

    J. M. Bardeen, P. J. Steinhardt, and M. S. Turner, Phys. Rev.D28, 679 (1983)

    1983

  16. [16]

    Komatsu and C

    E. Komatsu and C. L. Bennett (WMAP Science Team), PTEP2014, 06B102 (2014), arXiv:1404.5415 [astro- ph.CO]

    Pith/arXiv arXiv 2014

  17. [17]

    Bartolo, E

    N. Bartolo, E. Komatsu, S. Matarrese, and A. Riotto, Phys. Rept.402, 103 (2004), arXiv:astro-ph/0406398

    Pith/arXiv arXiv 2004

  18. [18]

    J. M. Maldacena, JHEP2003(05), 013, arXiv:astro- ph/0210603

    arXiv

  19. [19]

    Chen, Adv

    X. Chen, Adv. Astron.2010, 638979 (2010), arXiv:1002.1416 [astro-ph.CO]

    Pith/arXiv arXiv 2010

  20. [20]

    Desjacques and U

    V. Desjacques and U. Seljak, Class. Quant. Grav.27, 124011 (2010), arXiv:1003.5020 [astro-ph.CO]

    Pith/arXiv arXiv 2010

  21. [21]

    Komatsu, Class

    E. Komatsu, Class. Quant. Grav.27, 124010 (2010), arXiv:1003.6097 [astro-ph.CO]

    Pith/arXiv arXiv 2010

  22. [22]

    Furlanetto, S

    S. Furlanetto, S. P. Oh, and F. Briggs, Phys. Rept.433, 181 (2006), arXiv:astro-ph/0608032

    Pith/arXiv arXiv 2006

  23. [23]

    Abdurashidovaet al.(HERA), Astrophys

    Z. Abdurashidovaet al.(HERA), Astrophys. J.998, 33 (2026), arXiv:2511.21289 [astro-ph.CO]

    arXiv 2026

  24. [24]

    W. Qin, K. Schutz, A. Smith, E. Garaldi, R. Kannan, T. R. Slatyer, and M. Vogelsberger, Phys. Rev. D106, 123506 (2022), arXiv:2205.06270 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  25. [25]

    Andrews, J

    A. Andrews, J. Jasche, G. Lavaux, and F. Schmidt, Mon. Not. Roy. Astron. Soc.520, 5746 (2023), arXiv:2203.08838 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  26. [26]

    Nguyen, F

    N.-M. Nguyen, F. Schmidt, B. Tucci, M. Reinecke, and A. Kosti´ c, Phys. Rev. Lett.133, 221006 (2024), arXiv:2403.03220 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  27. [27]

    Andrewset al., arXiv e-Prints (2026), arXiv:2603.20855 [astro-ph.CO]

    A. Andrewset al., arXiv e-Prints (2026), arXiv:2603.20855 [astro-ph.CO]

    arXiv 2026

  28. [28]

    M. M. Anber and L. Sorbo, Phys. Rev. D81, 043534 (2010), arXiv:0908.4089 [hep-th]

    Pith/arXiv arXiv 2010

  29. [29]

    Maleknejad, M

    A. Maleknejad, M. M. Sheikh-Jabbari, and J. Soda, Phys. Rept.528, 161 (2013), arXiv:1212.2921 [hep-th]

    Pith/arXiv arXiv 2013

  30. [30]

    Pajer and M

    E. Pajer and M. Peloso, Class. Quant. Grav.30, 214002 (2013), arXiv:1305.3557 [hep-th]

    Pith/arXiv arXiv 2013

  31. [31]

    Caravano, E

    A. Caravano, E. Komatsu, K. D. Lozanov, and J. Weller, Phys. Rev. D108, 043504 (2023), arXiv:2204.12874 [astro-ph.CO]. 10

    Pith/arXiv arXiv 2023

  32. [32]

    D. G. Figueroa, J. Lizarraga, A. Urio, and J. Urrestilla, Phys. Rev. Lett.131, 151003 (2023), arXiv:2303.17436 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  33. [33]

    D. G. Figueroa, J. Lizarraga, N. Loayza, A. Urio, and J. Urrestilla, Phys. Rev. D111, 063545 (2025), arXiv:2411.16368 [astro-ph.CO]

    arXiv 2025

  34. [34]

    Sharma, A

    R. Sharma, A. Brandenburg, K. Subramanian, and A. Vikman, JCAP05(2025), 079, arXiv:2411.04854 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  35. [35]

    Iarygina, E

    O. Iarygina, E. I. Sfakianakis, and A. Brandenburg, arXiv e-Prints (2025), arXiv:2506.20538 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  36. [36]

    Jamieson, A

    D. Jamieson, A. Caravano, and E. Komatsu, Phys. Rev. D112, 103531 (2025), arXiv:2507.22285 [astro-ph.CO]

    arXiv 2025

  37. [37]

    Scoccimarro, L

    R. Scoccimarro, L. Hui, M. Manera, and K. C. Chan, Phys. Rev. D85, 083002 (2012), arXiv:1108.5512 [astro- ph.CO]

    Pith/arXiv arXiv 2012

  38. [38]

    W. R. Coulton, F. Villaescusa-Navarro, D. Jamieson, M. Baldi, G. Jung, D. Karagiannis, M. Liguori, L. Verde, and B. D. Wandelt, Astrophys. J.943, 64 (2023), arXiv:2206.01619 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  39. [39]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. D67, 123504 (2003), arXiv:astro-ph/0302326

    Pith/arXiv arXiv 2003

  40. [40]

    Barnaby and M

    N. Barnaby and M. Peloso, Phys. Rev. Lett.106, 181301 (2011), arXiv:1011.1500 [hep-ph]

    Pith/arXiv arXiv 2011

  41. [41]

    M. M. Anber and L. Sorbo, Phys. Rev. D85, 123537 (2012), arXiv:1203.5849 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  42. [42]

    E. V. Gorbar, K. Schmitz, O. O. Sobol, and S. I. Vilchin- skii, Phys. Rev. D104, 123504 (2021), arXiv:2109.01651 [hep-ph]

    Pith/arXiv arXiv 2021

  43. [43]

    Peloso and L

    M. Peloso and L. Sorbo, JCAP2023(01), 038, arXiv:2209.08131 [astro-ph.CO]

    Pith/arXiv arXiv

  44. [44]

    Barbon, N

    M. Barbon, N. Ijaz, and M. Peloso, JCAP2026(06), 013, arXiv:2510.17207 [astro-ph.CO]

    arXiv

  45. [45]

    D. Blas, J. Lesgourgues, and T. Tram, JCAP2011(07), 034, arXiv:1104.2933 [astro-ph.CO]

    Pith/arXiv arXiv

  46. [46]

    Michaux, O

    M. Michaux, O. Hahn, C. Rampf, and R. E. An- gulo, Mon. Not. Roy. Astron. Soc.500, 663 (2020), arXiv:2008.09588 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  47. [47]

    Springel, R

    V. Springel, R. Pakmor, O. Zier, and M. Rei- necke, Mon. Not. Roy. Astron. Soc.506, 2871 (2021), arXiv:2010.03567 [astro-ph.IM]

    Pith/arXiv arXiv 2021

  48. [48]

    Kallosh, A

    R. Kallosh, A. Linde, and D. Roest, JHEP11, 198, arXiv:1311.0472 [hep-th]

    Pith/arXiv arXiv

  49. [49]

    Akramiet al.(Planck), Astron

    Y. Akramiet al.(Planck), Astron. Astrophys.641, A9 (2020), arXiv:1905.05697 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  50. [50]

    LoVerde and K

    M. LoVerde and K. M. Smith, JCAP2011(08), 003, arXiv:1102.1439 [astro-ph.CO]

    Pith/arXiv arXiv

  51. [51]

    J. L. Tinker, A. V. Kravtsov, A. Klypin, K. Abazajian, M. S. Warren, G. Yepes, S. Gottlober, and D. E. Holz, Astrophys. J.688, 709 (2008), arXiv:0803.2706 [astro- ph]

    Pith/arXiv arXiv 2008

  52. [52]

    H. Mo, F. C. van den Bosch, and S. White,Galaxy Formation and Evolution(Cambridge University Press, 2010)

    2010

  53. [53]

    Lucchin and S

    F. Lucchin and S. Matarrese, Astrophys. J.330, 535 (1988)

    1988

  54. [54]

    Matarrese, L

    S. Matarrese, L. Verde, and R. Jimenez, Astrophys. J. 541, 10 (2000), arXiv:astro-ph/0001366

    Pith/arXiv arXiv 2000

  55. [55]

    W. H. Press and P. Schechter, Astrophys. J.187, 425 (1974)

    1974

  56. [56]

    Labb´ e, P

    I. Labb´ e, P. van Dokkum, E. Nelson, R. Bezanson, K. A. Suess, J. Leja, G. Brammer, K. Whitaker, E. Mathews, M. Stefanon, and B. Wang, Nature (London)616, 266 (2023), arXiv:2207.12446 [astro-ph.GA]

    Pith/arXiv arXiv 2023

  57. [57]

    Boylan-Kolchin, Nature Astron.7, 731 (2023), arXiv:2208.01611 [astro-ph.CO]

    M. Boylan-Kolchin, Nature Astron.7, 731 (2023), arXiv:2208.01611 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  58. [58]

    Blamart, A

    M. Blamart, A. Liu, R. Brandenberger, J. B. Mu˜ noz, and B. Cyr, Phys. Rev. D114, 023523 (2026), arXiv:2512.09980 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  59. [59]

    Mattheeet al., Astrophys

    J. Mattheeet al., Astrophys. J.963, 129 (2024), arXiv:2306.05448 [astro-ph.GA]

    Pith/arXiv arXiv 2024

  60. [60]

    J. E. Greene, I. Labbe, A. D. Goulding, L. J. Furtak, I. Chemerynska, V. Kokorev,et al., Astrophys. J.964, 39 (2024), arXiv:2309.05714 [astro-ph.GA]

    Pith/arXiv arXiv 2024