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The paper forecasts that measuring the 21cm brightness-temperature variance with upcoming radio arrays can constrain the cold-dark-matter isocurvature fraction to about 3e-4, a new sub-percent probe of inflationary initial conditions.

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2026-08-04 16:13 UTC pith:6SAOPTLE

load-bearing objection A useful first forecast of 21cm one-point statistics for CDM isocurvature; the qualitative timing shifts look robust, but the sub-percent headline is conditional on an astrophysical model the Fisher analysis never marginalizes over. the 3 major comments →

arxiv 2509.14751 v2 pith:6SAOPTLE submitted 2025-09-18 astro-ph.CO

Probing initial isocurvature perturbation with 21cm one-point statistics

Zhenfei Qin , Hayato Shimabukuro This is my paper
classification astro-ph.CO
keywords isocurvature perturbations21cm linecosmic dawnepoch of reionizationbrightness temperature varianceskewnessFisher forecastSKA
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.

The paper claims that one-point statistics of the 21cm hydrogen line, measured during the Cosmic Dawn and Epoch of Reionization, can detect and measure a cold dark matter isocurvature component in the primordial perturbations. The central quantitative forecast is that the variance of the 21cm brightness temperature, observed with SKA Phase 1-like sensitivity, constrains the isocurvature fraction to about 3e-4, while the skewness does so an order of magnitude more weakly. The physical signature is that even a few percent isocurvature fraction shifts the timing of key cosmic milestones, Wouthuysen-Field coupling, X-ray heating, and reionization, by more than one unit of redshift, an effect clearly visible in variance peaks. If correct, this provides a new, independent window on the physics of inflation that complements CMB constraints, although a degeneracy between the isocurvature fraction and its spectral index remains.

Core claim

The authors show that adding a CDM isocurvature component to the standard adiabatic perturbations enhances small-scale matter clustering, advancing the epochs of first light, X-ray heating, and reionization. This moves the peaks in the 21cm variance, and the sign-change redshift of the skewness, to higher redshift while leaving their amplitudes nearly unchanged. Using a Fisher-matrix forecast based on the redshift evolution of variance and skewness of 12 Mpc-smoothed 21cm maps with SKA-level thermal noise, they find that variance alone constrains the isocurvature fraction to Delta r_CDM ~ 3e-4 and the spectral index to Delta n_iso ~ 1.4e-3, while skewness yields values an order of magnitude

What carries the argument

The central machinery is the one-point variance and skewness of the 21cm brightness temperature field, computed from semi-numerical simulations over 300 Mpc boxes, smoothed to 12 Mpc to match the interferometer beam, and with thermal noise added to match SKA Phase 1. The Fisher-matrix forecast uses the redshift evolution of these statistics as the data vector, assuming Gaussian likelihoods and uncorrelated redshift bins, with errors given by the thermal noise floor.

Load-bearing premise

The forecast treats the per-redshift error as purely thermal noise after 12 Mpc smoothing and assumes redshift bins are independent, so the real cosmic variance of the single 300 Mpc simulation box could weaken the stated constraints.

What would settle it

Compute the variance of the 21cm variance estimator across many independent 300 Mpc simulated volumes at z=7-15; if this sample variance is comparable to or larger than the SKA thermal noise floor at those redshifts, the claimed Delta r_CDM ~ 3e-4 is over-optimistic and the central forecast would fail.

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

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If this is right

  • If SKA Phase 1 observes 1000 hours, variance measurements over z~7-15 could constrain the CDM isocurvature fraction to sub-percent precision, extending CMB constraints to small scales where blue-tilted isocurvature spectra are most prominent.
  • The systematic timing shift of variance peaks (Delta z > 1) offers a diagnostic that is relatively insensitive to astrophysical modeling compared to skewness, which is strongly affected by X-ray heating assumptions.
  • Skewness alone cannot disentangle isocurvature from astrophysical heating; it must be combined with variance or other probes to be useful.
  • The residual degeneracy between r_CDM and n_iso means 21cm one-point statistics alone cannot independently measure both parameters; complementary probes such as the 21cm forest or galaxy surveys will be needed.
  • Because the Fisher formalism underestimates information content of non-Gaussian statistics, simulation-based inference may yield constraints even tighter than the quoted forecasts.

Where Pith is reading between the lines

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

  • Testable extension: the same analysis technique applied to the full distribution of brightness temperatures (or to higher moments like kurtosis) might break the r_CDM-n_iso degeneracy without requiring external data sets.
  • Editorial inference: the forecast neglects sample variance from the finite simulation volume, so an ensemble of independent 300 Mpc boxes would likely widen the quoted error bars; this is a conservative caveat rather than a model uncertainty.
  • The bimodal PDF feature appearing shortly after Wouthuysen-Field coupling (a secondary peak from X-ray-heated islands) could serve as a direct imaging signature of isocurvature, independent of power-spectrum statistics.
  • Editorial inference: if variance peak positions prove robust across astrophysical models, they could act as a 'redshift ruler' for early structure formation, potentially constraining other early-universe physics such as primordial non-Gaussianity or warm dark matter.

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. Using 21cmFAST simulations of a 300 cMpc box with 200^3 cells, the authors model adiabatic plus CDM isocurvature initial conditions with power-spectrum ratio r_CDM and spectral index n_iso. They compute 21cm power spectra, variance, and skewness from z~30 to 6 for three HERA-motivated astrophysical models, add SKA thermal noise with 12 Mpc smoothing, and run a Fisher forecast on the redshift evolution of variance and skewness. They report that increasing r_CDM advances WF coupling, X-ray heating, and reionization, shifting variance peaks by Δz≈2.8 (reionization) and Δz≈8.7 (X-ray) for r_CDM 0→0.1; that variance alone gives Δr_CDM≈3×10^-4 and skewness gives Δr_CDM≈3×10^-3; and that a strong r_CDM–n_iso degeneracy remains.

Significance. If the forecasts hold, this would be a genuinely new probe: 21cm one-point statistics at SKA Phase-1 sensitivity could constrain blue-tilted CDM isocurvature modes on scales poorly probed by the CMB. The qualitative timing-shift result is interesting and likely robust, since it is physically well motivated and consistently appears in power spectra, variance, and skewness. The paper is transparent in using a public simulation code, three astrophysical models, and SKA noise, and it identifies the Gaussian-likelihood and foreground limitations. The quantitative sub-percent constraint, however, is more fragile than the paper's headline states, because the Fisher forecast ignores sample variance and marginalizes only a subset of the astrophysical parameters that the paper itself shows shift the observables by comparable amounts.

major comments (3)
  1. [§III D, Eq. (13), Fig. 8] The forecast takes σ_k to be SKA thermal noise only and assumes independent redshift bins. For a single 300 cMpc simulation box, the variance and skewness estimators have their own cosmic/sample variance. After smoothing to R_smooth=12 Mpc, there are only ~(300/12)^3≈1.6×10^4 independent cells per redshift; the relative sample variance of the variance estimator is ~(2/N_eff)^{1/2}, which for variance values of tens of mK² in Fig. 8 can be comparable to or larger than the plotted SKA error band. Omitting this term makes the quoted Δr_CDM≃3×10^-4 a lower bound under idealized assumptions. Please add a sample-variance contribution (or a quantitative argument that it is subdominant) and recompute the Fisher errors.
  2. [§III D and Fig. 6] The Fisher matrix (Eq. 13) varies only r_CDM, n_iso, and log10(L_X/SFR), fixing α_*, M_turn, and t_* at Model 1. The top panel of Fig. 6 shows that moving among the three HERA-motivated models changes the variance peak positions and amplitudes by amounts comparable to the isocurvature shifts in the bottom panel; e.g. Model 3 moves the reionization peak out of the plotted range and Model 2 shifts the X-ray peak to higher z. Since isocurvature acts mainly by advancing halo formation and star formation, the variance signature is partially degenerate with these fixed astrophysical parameters. The forecast therefore conditions the 3×10^-4 constraint on an exact astrophysical model rather than on realistic astrophysical ignorance. Please include α_*, M_turn, t_* in the Fisher forecast (with priors from HERA if desired) or otherwise demonstrate that the headline constraint survives marginalizat
  3. [§III C/D, Eq. (16)] The skewness uncertainty used in Fig. 8 follows from a variance-propagation formula, but the paper does not specify how V_{\hat S_2}, V_{\hat S_3}, and Cov(\hat S_2,\hat S_3) are computed—in particular how thermal noise, smoothing-induced correlations, sample variance, and the finite simulation volume enter. The claim that the first term dominates and produces the z≈10 bump drives the skewness Fisher result, so this is not a minor technicality. Please specify the estimator covariance calculation or state the assumptions under which Eq. (16) is evaluated.
minor comments (4)
  1. [Abstract] The abstract says the isocurvature fraction can be constrained to 'the percent level', while the full-text abstract and Section V quote 'sub-percent' (3×10^-4). Please harmonize.
  2. [§III B, Eqs. (6)–(9)] The definitions of variance and skewness do not mention the smoothing scale; the simulated values appear to be computed on smoothed maps (Section IV C). Please make this explicit in the definitions.
  3. [Fig. 8] The shaded region is described as 1σ instrumental noise, but the text states the data are noise-limited for z≳15. Please clarify whether the shaded region is the error on the measured statistic or the map-level noise, and how the smoothing affects the noise for variance and skewness separately.
  4. [Fig. 9] The contour axes are normalized by fiducial values without showing the physical values on the axes. Adding the physical parameter values would improve readability.

Circularity Check

0 steps flagged

No significant circularity: the SKA forecast is a forward Fisher calculation from an external HERA-anchored astrophysical model; self-citations are background only.

full rationale

The paper's claimed result (variance forecasts Δr_CDM ≃ 3×10^-4) is a Fisher forecast from simulated 21cm maps. The chain is: Eq. (2) defines the isocurvature spectrum; Eq. (3) sums adiabatic and isocurvature matter power; 21cmFAST converts this into δTb maps; Eqs. (8)-(9) define variance and skewness; Eqs. (10)-(11) add SKA thermal noise; Eq. (13) is the Fisher matrix. Every step is a forward model, not a fit to the forecasted quantity. The astrophysical parameters (Table I) are anchored to external HERA observations [63], not to the 21cm one-point statistics being predicted, and no parameter is fitted to the variance/skewness curves and then re-predicted. The author's self-citations ([20], [22]-[24], [26], [70]-[75]) are used for background definitions, peak identifications, and suggested complementary probes; none carries the load of the central forecast. The acknowledged limitations—Section V states the Fisher formalism assumes Gaussian likelihoods and that real observations face foregrounds and systematics, and the forecast fixes α*, M_turn, t* while varying only r_CDM, n_iso, log10(LX/SFR)—make the quantitative bound conditional on model assumptions, but they do not make the result circular. No equation reduces to an input by construction, and no fitted parameter is renamed as a prediction. Therefore no circular step is identified.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

The forecast rests on standard assumptions (linear transfer functions, uncorrelated modes, 21cmFAST fidelity) and on fiducial parameter choices that are not constrained by data in this paper. The most fragile input is the neglect of sample variance, which directly controls the quoted precision.

free parameters (5)
  • r_CDM (isocurvature fraction) = fiducial 0.05
    Chosen fiducial value for the Fisher forecast; the central claim is the precision with which this can be measured.
  • n_iso (isocurvature spectral index) = fiducial 2.5
    Chosen fiducial value; strongly degenerate with r_CDM and varied in the Fisher analysis.
  • log10(LX<2.0keV/SFR) (X-ray heating efficiency) = fiducial 40.64 erg/s/M_sun/yr
    Astrophysical nuisance parameter included in the Fisher forecast; affects variance and skewness timing and amplitude.
  • Astrophysical model parameters (alpha*, Mturn, t*) for models 1-3 = Table I values
    Taken from HERA-constrained models, used as fixed inputs; variations among models change the variance/skewness redshift evolution and affect the forecast's robustness.
  • Smoothing scale Rsmooth = 12 Mpc
    Chosen by hand to match the SKA beam; directly affects the noise level and the variance/skewness values, so the forecast numbers depend on this choice.
axioms (7)
  • domain assumption Adiabatic and CDM isocurvature perturbations are uncorrelated and add linearly in the matter power spectrum (Eq. 3).
    Standard in the literature but not universally true for all inflation models; the forecast does not explore correlated modes.
  • domain assumption The isocurvature power spectrum is a pure power law with free spectral index n_iso (Eq. 2).
    Assumed form from inflation model expectations; a different shape could change the small-scale enhancement and the forecast.
  • standard math Transfer functions T_adi(k) and T_iso(k) from Refs. [31,32] correctly describe the linear evolution of perturbations.
    Well-established linear perturbation theory, relied upon without re-derivation.
  • domain assumption 21cmFAST semi-numerical simulations adequately capture the 21cm signal from Cosmic Dawn and EoR.
    The entire analysis depends on the fidelity of 21cmFAST, which uses simplified radiative transfer and astrophysical recipes.
  • domain assumption The SKA thermal noise model (Eqs. 10-11) and the Haslam sky temperature relation are representative of the actual instrument.
    Noise is modeled analytically; foregrounds, calibration errors, and RFI are explicitly neglected.
  • domain assumption Fisher matrix formalism with Gaussian likelihood and independent redshift bins applies (Eq. 13).
    The paper states this assumption and acknowledges that non-Gaussian statistics may not be captured; it is a standard but restrictive approximation.
  • ad hoc to paper Sample variance (cosmic variance) of variance and skewness estimators is negligible relative to thermal noise.
    This assumption is never stated explicitly; the error bars in the Fisher forecast derive from thermal noise only, despite using a single 300 Mpc simulation box.

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Cite this review

Pith. "Pith review of Probing initial isocurvature perturbation with 21cm one-point statistics." pith.science (2026). https://pith.science/paper/6SAOPTLE

@misc{pith2026250914751,
  author       = {Pith},
  title        = {Pith review of: Probing initial isocurvature perturbation with 21cm one-point statistics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6SAOPTLE}},
  note         = {Machine review of arXiv:2509.14751}
}
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read the original abstract

Isocurvature perturbation--expected from multi-field inflation models--can leave unique signatures in the early Universe, but remain weakly constrained, especially on small scales. In this work, we investigate the constraining power of one-point statistics (variance and skewness) of the 21cm brightness temperature during Cosmic Dawn and the Epoch of Reionization, using semi-numerical simulations from 21cmFAST. We model both adiabatic and cold dark matter isocurvature modes, exploring their impact on the matter power spectrum, the timing of structure formation, and the evolution of neutral hydrogen. By varying astrophysical parameters as well as the isocurvature fraction and spectral index, we quantify their respective effects on the 21cm power spectrum and on one-point statistics, using the former as a physical diagnostic and the latter as the basis of our final forecast. Our results show that while variance is highly sensitive to the timing of cosmic events and provides tight constraints on isocurvature parameters, skewness is more strongly affected by astrophysical uncertainties and observational noise. Incorporating realistic instrumental noise based on SKA configurations, we perform a Fisher analysis using only the redshift evolution of the one-point statistics, and demonstrate that the isocurvature fraction can be constrained down to the percent level, though a strong degeneracy with the spectral index remains. We discuss the importance of complementary probes, such as the 21cm forest and galaxy surveys, to break these parameter degeneracies. Our findings highlight the power of 21cm one-point statistics as robust and independent tools for probing early-Universe physics beyond what is accessible with traditional power spectrum analyses.

Figures

Figures reproduced from arXiv: 2509.14751 by Hayato Shimabukuro, Zhenfei Qin.

Figure 2
Figure 2. Figure 2: FIG. 2: The theoretically predicted history of the neutral frac [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: From up to bottom: Maps of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Illustration of the 21cm power spectrum for three [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Top: PDF in adiabatic case. Bottom: PDF with [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Top: Variance of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The variance (top) and skewness (bottom) of bright [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: 1- [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

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

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Reference graph

Works this paper leans on

86 extracted references · 3 canonical work pages · cited by 1 Pith paper

  1. [1]

    Akrami, F

    Planck Collaboration, Y. Akrami, F. Arroja, M. Ash- down, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, et al., A&A641, A10 (2020), 1807.06211

    Pith/arXiv arXiv 2020

  2. [2]

    Conversely, lower X-ray efficiencies yield a slower evolution and stronger skewness signatures

    produce larger local temperature enhancements ear- lier, driving an earlier zero-crossing and rising to posi- tive skewness. Conversely, lower X-ray efficiencies yield a slower evolution and stronger skewness signatures. In- creasingr CDM shifts the skewness peak toward higher redshifts, again reflecting earlier structure formation and heating. However, b...

  3. [3]

    Komatsu, K

    E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, G. Hinshaw, N. Jarosik, D. Larson, M. R. Nolta, L. Page, et al., ApJS192, 18 (2011), 1001.4538

    Pith/arXiv arXiv 2011

  4. [4]

    Bucher, K

    M. Bucher, K. Moodley, and N. Turok, Phys. Rev. D 62, 083508 (2000), URLhttps://link.aps.org/doi/ 10.1103/PhysRevD.62.083508

    work page doi:10.1103/physrevd.62.083508 2000

  5. [5]

    V¨ aliviita and T

    J. V¨ aliviita and T. Giannantonio, Phys. Rev. D80, 123516 (2009), 0909.5190

    Pith/arXiv arXiv 2009

  6. [6]

    Kasuya and M

    S. Kasuya and M. Kawasaki, Physical Review D80 (2009), ISSN 1550-2368, URLhttp://dx.doi.org/10. 1103/PhysRevD.80.023516

    2009

  7. [7]

    D. J. Chung and H. Yoo, Physical Review D91 (2015), ISSN 1550-2368, URLhttp://dx.doi.org/10. 1103/PhysRevD.91.083530

    2015

  8. [8]

    D. J. Chung and A. Upadhye, Physical Review D98 (2018), ISSN 2470-0029, URLhttp://dx.doi.org/10. 1103/PhysRevD.98.023525

    2018

  9. [9]

    D. J. Chung and S. C. Tadepalli, Physical Review D105 (2022), ISSN 2470-0029, URLhttp://dx.doi.org/10. 1103/PhysRevD.105.123511

    2022

  10. [10]

    Afshordi, P

    N. Afshordi, P. McDonald, and D. N. Spergel, The Astro- physical Journal594, L71–L74 (2003), ISSN 1538-4357, URLhttp://dx.doi.org/10.1086/378763

    doi:10.1086/378763 2003

  11. [11]

    Kashlinsky, The Astrophysical Journal Letters823, L25 (2016), ISSN 2041-8213, URLhttp://dx.doi.org/ 10.3847/2041-8205/823/2/L25

    A. Kashlinsky, The Astrophysical Journal Letters823, L25 (2016), ISSN 2041-8213, URLhttp://dx.doi.org/ 10.3847/2041-8205/823/2/L25

    work page doi:10.3847/2041-8205/823/2/l25 2016

  12. [13]

    Gong and N

    J.-O. Gong and N. Kitajima, Journal of Cosmology and Astroparticle Physics2018, 041–041 (2018), ISSN 1475- 7516, URLhttp://dx.doi.org/10.1088/1475-7516/ 2018/11/041

    doi:10.1088/1475-7516/ 2018

  13. [14]

    O. Mena, S. Palomares-Ruiz, P. Villanueva-Domingo, and S. J. Witte, Physical Review D100(2019), ISSN 2470-0029, URLhttp://dx.doi.org/10.1103/ PhysRevD.100.043540

    2019

  14. [15]

    Tashiro and K

    H. Tashiro and K. Kadota, Physical Review D104 (2021), ISSN 2470-0029, URLhttp://dx.doi.org/10. 1103/PhysRevD.104.063522

    2021

  15. [16]

    A. R. Liddle and A. Mazumdar, Phys. Rev. D61, 123507 (2000), astro-ph/9912349

    Pith/arXiv arXiv 2000

  16. [17]

    Gordon, D

    C. Gordon, D. Wands, B. A. Bassett, and R. Maartens, Physical review D: Particles and fields63, 398 (2000)

    2000

  17. [18]

    J. R. Pritchard and A. Loeb, Reports on Progress in Physics75, 086901 (2012), 1109.6012

    Pith/arXiv arXiv 2012

  18. [19]

    Hasegawa, S

    K. Hasegawa, S. Asaba, K. Ichiki, A. K. Inoue, S. Inoue, T. Ishiyama, H. Shimabukuro, K. Takahashi, H. Tashiro, H. Yajima, et al., arXiv e-prints arXiv:1603.01961 (2016), 1603.01961

    Pith/arXiv arXiv 2016

  19. [20]

    Yamauchi, K

    D. Yamauchi, K. Ichiki, K. Kohri, T. Namikawa, Y. Oyama, T. Sekiguchi, H. Shimabukuro, K. Takahashi, T. Takahashi, S. Yokoyama, et al., PASJ68, R2 (2016), 1603.01959

    Pith/arXiv arXiv 2016

  20. [21]

    Shimabukuro, K

    H. Shimabukuro, K. Hasegawa, A. Kuchinomachi, H. Ya- jima, and S. Yoshiura, PASJ75, S1 (2023), 2303.07594

    Pith/arXiv arXiv 2023

  21. [22]

    Minoda, S

    T. Minoda, S. Yoshiura, and T. Takahashi, Phys. Rev. D 105, 083523 (2022), 2112.15135

    Pith/arXiv arXiv 2022

  22. [23]

    Shimabukuro, S

    H. Shimabukuro, S. Yoshiura, K. Takahashi, S. Yokoyama, and K. Ichiki, MNRAS458, 3003 (2016), 1507.01335

    Pith/arXiv arXiv 2016

  23. [24]

    Kubota, S

    K. Kubota, S. Yoshiura, H. Shimabukuro, and K. Taka- hashi, PASJ68, 61 (2016), 1602.02873

    Pith/arXiv arXiv 2016

  24. [25]

    Shimabukuro, S

    H. Shimabukuro, S. Yoshiura, K. Takahashi, S. Yokoyama, and K. Ichiki, MNRAS468, 1542 (2017), 1608.00372

    Pith/arXiv arXiv 2017

  25. [26]

    C. A. Watkinson and J. R. Pritchard, MNRAS443, 3090 (2014), 1312.1342

    Pith/arXiv arXiv 2014

  26. [27]

    Shimabukuro, S

    H. Shimabukuro, S. Yoshiura, K. Takahashi, S. Yokoyama, and K. Ichiki, MNRAS451, 467 (2015), 1412.3332

    Pith/arXiv arXiv 2015

  27. [28]

    C. A. Watkinson and J. R. Pritchard, MNRAS454, 1416 (2015), 1505.07108

    Pith/arXiv arXiv 2015

  28. [29]

    Abdurashidova, J

    Z. Abdurashidova, J. E. Aguirre, P. Alexander, Z. S. Ali, Y. Balfour, R. Barkana, A. P. Beardsley, G. Bernardi, T. S. Billings, J. D. Bowman, et al., ApJ924, 51 (2022), 2108.07282

    Pith/arXiv arXiv 2022

  29. [30]

    Koopmans, J

    L. Koopmans, J. Pritchard, G. Mellema, J. Aguirre, K. Ahn, R. Barkana, I. van Bemmel, G. Bernardi, A. Bonaldi, F. Briggs, et al., inAdvancing Astrophysics with the Square Kilometre Array (AASKA14)(2015), 13 p. 1, 1505.07568

    Pith/arXiv arXiv 2015

  30. [31]

    M. P. van Haarlem, M. W. Wise, A. W. Gunst, G. Heald, J. P. McKean, J. W. T. Hessels, A. G. de Bruyn, R. Ni- jboer, J. Swinbank, R. Fallows, et al., A&A556, A2 (2013), 1305.3550

    Pith/arXiv arXiv 2013

  31. [32]

    J. M. Bardeen, J. R. Bond, N. Kaiser, and A. S. Szalay, ApJ304, 15 (1986)

    1986

  32. [33]

    Sugiyama, ApJS100, 281 (1995), astro-ph/9412025

    N. Sugiyama, ApJS100, 281 (1995), astro-ph/9412025

    Pith/arXiv arXiv 1995

  33. [34]

    Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Ar- naud, M. Ashdown, J. Aumont, C. Baccigalupi, A. J. Banday, R. B. Barreiro, J. G. Bartlett, et al., A&A594, A13 (2016), 1502.01589

    Pith/arXiv arXiv 2016

  34. [35]

    Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Ar- naud, F. Arroja, M. Ashdown, J. Aumont, C. Bacci- galupi, M. Ballardini, A. J. Banday, et al., A&A594, A17 (2016), 1502.01592

    Pith/arXiv arXiv 2016

  35. [36]

    M. R. Buckley, P. Du, N. Fernandez, and M. J. Weikert, General constraints on isocurvature from the cmb and ly- αforest(2025), 2502.20434, URLhttps://arxiv.org/ abs/2502.20434

    Pith/arXiv arXiv 2025

  36. [39]

    Konno, M

    A. Konno, M. Ouchi, Y. Ono, K. Shimasaku, T. Shibuya, H. Furusawa, K. Nakajima, Y. Naito, R. Momose, S. Yuma, et al., The Astrophysical Journal797, 16 (2014), URLhttps://dx.doi.org/10.1088/0004-637X/ 797/1/16

    doi:10.1088/0004-637x/ 2014

  37. [40]

    Zheng, J

    Z.-Y. Zheng, J. Wang, J. Rhoads, L. Infante, S. Malhotra, W. Hu, A. R. Walker, L. Jiang, C. Jiang, P. Hibon, et al., The Astrophysical Journal Letters842, L22 (2017), URL https://dx.doi.org/10.3847/2041-8213/aa794f

    doi:10.3847/2041-8213/aa794f 2017

  38. [41]

    A. K. Inoue, K. Hasegawa, T. Ishiyama, H. Yajima, I. Shimizu, M. Umemura, A. Konno, Y. Harikane, T. Shibuya, M. Ouchi, et al., PASJ70, 55 (2018), 1801.00067

    Pith/arXiv arXiv 2018

  39. [42]

    A. M. Morales, C. A. Mason, S. Bruton, M. Gronke, F. Haardt, and C. Scarlata, The Astrophysical Journal 919, 120 (2021), URLhttps://dx.doi.org/10.3847/ 1538-4357/ac1104

    2021

  40. [44]

    Y. Ning, L. Jiang, Z.-Y. Zheng, and J. Wu, The Astro- physical Journal926, 230 (2022), URLhttps://dx.doi. org/10.3847/1538-4357/ac4268

    doi:10.3847/1538-4357/ac4268 2022

  41. [45]

    Umeda, M

    H. Umeda, M. Ouchi, S. Kikuta, Y. Harikane, Y. Ono, T. Shibuya, A. K. Inoue, K. Shimasaku, Y. Liang, A. Matsumoto, et al.,Silverrush. xiv. lya luminosity func- tions and angular correlation functions from 20,000 lya emitters at z 2.2-7.3 from upto 24deg2 hsc-ssp and cho- rus surveys: Linking the post-reionization epoch to the heart of reionization(2024), ...

    Pith/arXiv arXiv 2024

  42. [46]

    Sobacchi and A

    E. Sobacchi and A. Mesinger, MNRAS453, 1843 (2015), 1505.02787

    Pith/arXiv arXiv 2015

  43. [47]

    Ouchi, Y

    M. Ouchi, Y. Harikane, T. Shibuya, K. Shimasaku, Y. Taniguchi, A. Konno, M. Kobayashi, M. Kajisawa, T. Nagao, Y. Ono, et al., PASJ70, S13 (2018), 1704.07455

    Pith/arXiv arXiv 2018

  44. [48]

    Umeda, M

    H. Umeda, M. Ouchi, K. Nakajima, Y. Harikane, Y. Ono, Y. Xu, Y. Isobe, and Y. Zhang, The Astrophysical Journal971, 124 (2024), URLhttps://dx.doi.org/10. 3847/1538-4357/ad554e

    2024

  45. [49]

    Curtis-Lake, S

    E. Curtis-Lake, S. Carniani, A. Cameron, S. Char- lot, P. Jakobsen, R. Maiolino, A. Bunker, J. Witstok, R. Smit, J. Chevallard, et al., Nature Astronomy7, 622 (2023), 2212.04568

    Pith/arXiv arXiv 2023

  46. [50]

    T. Y.-Y. Hsiao, Abdurro’uf, D. Coe, R. L. Larson, I. Jung, M. Mingozzi, P. Dayal, N. Kumari, V. Koko- rev, A. Vikaeus, et al.,Jwst nirspec spectroscopy of the triply-lensedz= 10.17galaxy macs0647−jd(2024), 2305.03042, URLhttps://arxiv.org/abs/2305.03042

    Pith/arXiv arXiv 2024

  47. [51]

    F. B. Davies, J. F. Hennawi, E. Ba˜ nados, Z. Luki´ c, R. Decarli, X. Fan, E. P. Farina, C. Mazzucchelli, H.-W. Rix, B. P. Venemans, et al., The Astrophysical Journal 864, 142 (2018), URLhttps://dx.doi.org/10.3847/ 1538-4357/aad6dc

    2018

  48. [52]

    Greig, A

    B. Greig, A. Mesinger, and E. Ba˜ nados, MNRAS484, 5094 (2019), 1807.01593

    Pith/arXiv arXiv 2019

  49. [54]

    Totani, N

    T. Totani, N. Kawai, G. Kosugi, K. Aoki, T. Yamada, M. Iye, K. Ohta, and T. Hattori, PASJ58, 485 (2006), astro-ph/0512154

    Pith/arXiv arXiv 2006

  50. [55]

    Totani, K

    T. Totani, K. Aoki, T. Hattori, G. Kosugi, Y. Niino, T. Hashimoto, N. Kawai, K. Ohta, T. Sakamoto, and T. Yamada, PASJ66, 63 (2014), 1312.3934

    Pith/arXiv arXiv 2014

  51. [56]

    A. Hoag, M. Bradaˇ c, K. Huang, C. Mason, T. Treu, K. B. Schmidt, M. Trenti, V. Strait, B. C. Lemaux, E. Q. Finney, et al., The Astrophysical Journal878, 12 (2019), URLhttps://dx.doi.org/10.3847/1538-4357/ ab1de7

    doi:10.3847/1538-4357/ 2019

  52. [57]

    J., Barreiro, R

    Planck Collaboration, Aghanim, N., Akrami, Y., Ash- down, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al., A&A641, A6 (2020), URLhttps://doi.org/10.1051/ 0004-6361/201833910

    2020

  53. [58]

    X. Fan, M. A. Strauss, R. H. Becker, R. L. White, J. E. Gunn, G. R. Knapp, G. T. Richards, D. P. Schnei- der, J. Brinkmann, and M. Fukugita, The Astronomical Journal132, 117 (2006), URLhttps://dx.doi.org/10. 1086/504836

    2006

  54. [59]

    S. R. Furlanetto, S. Peng Oh, and F. H. Briggs, Physics Reports433, 181 (2006), ISSN 0370-1573, URL https://www.sciencedirect.com/science/article/ pii/S0370157306002730

    2006

  55. [60]

    Barkana and A

    R. Barkana and A. Loeb, MNRAS384, 1069 (2008), 0705.3246

    Pith/arXiv arXiv 2008

  56. [61]

    G. J. A. Harker, S. Zaroubi, R. M. Thomas, V. Jeli´ c, P. Labropoulos, G. Mellema, I. T. Iliev, G. Bernardi, M. A. Brentjens, A. G. de Bruyn, et al., MNRAS393, 1449 (2009), 0809.2428

    Pith/arXiv arXiv 2009

  57. [62]

    Mesinger and S

    A. Mesinger and S. Furlanetto, ApJ669, 663 (2007), 0704.0946

    Pith/arXiv arXiv 2007

  58. [63]

    Mesinger, S

    A. Mesinger, S. Furlanetto, and R. Cen, MNRAS411, 955 (2011), 1003.3878. 14

    Pith/arXiv arXiv 2011

  59. [64]

    J. Park, A. Mesinger, B. Greig, and N. Gillet, Monthly Notices of the Royal Astronomical Society484, 933–949 (2019), ISSN 1365-2966, URLhttp://dx.doi.org/10. 1093/mnras/stz032

    2019

  60. [65]

    C. G. T. Haslam, C. J. Salter, H. Stoffel, and W. E. Wilson, A&AS47, 1 (1982)

    1982

  61. [66]

    Coe, arXiv e-prints arXiv:0906.4123 (2009), 0906.4123

    D. Coe, arXiv e-prints arXiv:0906.4123 (2009), 0906.4123

    Pith/arXiv arXiv 2009

  62. [67]

    Verde,Statistical Methods in Cosmology(Springer Berlin Heidelberg, Berlin, Heidelberg, 2010), pp

    L. Verde,Statistical Methods in Cosmology(Springer Berlin Heidelberg, Berlin, Heidelberg, 2010), pp. 147– 177, ISBN 978-3-642-10598-2, URLhttps://doi.org/ 10.1007/978-3-642-10598-2_4

    work page doi:10.1007/978-3-642-10598-2_4 2010

  63. [68]

    Prelogovi´ c and A

    D. Prelogovi´ c and A. Mesinger, MNRAS524, 4239 (2023), 2305.03074

    Pith/arXiv arXiv 2023

  64. [69]

    X. Zhao, Y. Mao, S. Zuo, and B. D. Wandelt, ApJ973, 41 (2024), 2310.17602

    Pith/arXiv arXiv 2024

  65. [70]

    T.-Y. Sun, Y. Shao, Y. Li, Y. Xu, H. Wang, and X. Zhang, Communications Physics8, 220 (2025), 2407.14298

    Pith/arXiv arXiv 2025

  66. [71]

    Shimabukuro, K

    H. Shimabukuro, K. Ichiki, S. Inoue, and S. Yokoyama, Phys. Rev. D90, 083003 (2014), 1403.1605

    Pith/arXiv arXiv 2014

  67. [72]

    Shimabukuro, K

    H. Shimabukuro, K. Ichiki, and K. Kadota, Phys. Rev. D 101, 043516 (2020), 1910.06011

    Pith/arXiv arXiv 2020

  68. [73]

    Shimabukuro, K

    H. Shimabukuro, K. Ichiki, and K. Kadota, Phys. Rev. D 102, 023522 (2020), 2005.05589

    Pith/arXiv arXiv 2020

  69. [74]

    Shimabukuro, K

    H. Shimabukuro, K. Ichiki, and K. Kadota, Phys. Rev. D 107, 123520 (2023), 2212.08409

    Pith/arXiv arXiv 2023

  70. [75]

    Y. Shao, Y. Xu, Y. Wang, W. Yang, R. Li, X. Zhang, and X. Chen, Nature Astronomy7, 1116 (2023), 2307.04130

    Pith/arXiv arXiv 2023

  71. [76]

    Shimabukuro, Y

    H. Shimabukuro, Y. Xu, and Y. Shao, arXiv e-prints arXiv:2504.14656 (2025), 2504.14656

    arXiv 2025

  72. [77]

    ˇSoltinsk´ y, G

    T. ˇSoltinsk´ y, G. Kulkarni, S. P. Tendulkar, and J. S. Bolton, MNRAS537, 364 (2025), 2412.06879

    Pith/arXiv arXiv 2025

  73. [78]

    Shao, G.-H

    Y. Shao, G.-H. Du, T.-N. Li, and X. Zhang, Physics Let- ters B862, 139342 (2025), 2501.00769

    Pith/arXiv arXiv 2025

  74. [79]

    Liu and M

    A. Liu and M. Tegmark, Phys. Rev. D83, 103006 (2011), 1103.0281

    Pith/arXiv arXiv 2011

  75. [80]

    Petrovic and S

    N. Petrovic and S. P. Oh, MNRAS413, 2103 (2011), 1010.4109

    Pith/arXiv arXiv 2011

  76. [81]

    Majumdar, J

    S. Majumdar, J. R. Pritchard, R. Mondal, C. A. Watkin- son, S. Bharadwaj, and G. Mellema, MNRAS476, 4007 (2018), 1708.08458

    Pith/arXiv arXiv 2018

  77. [82]

    C. A. Watkinson, S. K. Giri, H. E. Ross, K. L. Dixon, I. T. Iliev, G. Mellema, and J. R. Pritchard, MNRAS 482, 2653 (2019), 1808.02372

    Pith/arXiv arXiv 2019

  78. [83]

    Hutter, C

    A. Hutter, C. A. Watkinson, J. Seiler, P. Dayal, M. Sinha, and D. J. Croton, MNRAS492, 653 (2020), 1907.04342

    Pith/arXiv arXiv 2020

  79. [84]

    Yoshiura, H

    S. Yoshiura, H. Shimabukuro, K. Takahashi, and T. Mat- subara, MNRAS465, 394 (2017), 1602.02351

    Pith/arXiv arXiv 2017

  80. [85]

    Z. Chen, Y. Xu, Y. Wang, and X. Chen, ApJ885, 23 (2019), 1812.10333

    Pith/arXiv arXiv 2019

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.