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The ISW effect is detected at 2.8σ in Quaia quasar–Planck CMB cross-correlations, with amplitude 1.69 ± 0.61, and the evolving-dark-energy models preferred by recent BAO and lensing data cannot explain the excess.

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A 2.8σ detection of the integrated Sachs-Wolfe effect in the Quaia×Planck cross-correlation gives A_ISW = 1.69 ± 0.61, moderately above ΛCDM and unexplained by current CPL dark-energy models.

T0 review reviewed 2026-08-01 challenge →

load-bearing objection A careful new ISW measurement from Quaia, but the headline 2.8σ is softer than it looks — the linear-regime cut gives 2.1σ, and the amplitude is sensitive to the bias model; still worth sending to a referee. the 3 major comments →

arxiv 2607.22461 v1 pith:SYMLK2LL submitted 2026-07-24 astro-ph.CO

Probing dark energy evolution with Quaia quasars through the integrated Sachs-Wolfe effect

M. Ghodsi Yengejeh , J. R. Bermejo-Climent , A. Kov\'acs , I. Szapudi , I. Csabai This is my paper
classification astro-ph.CO
keywords integrated Sachs-Wolfe effectISWQuaia quasarsCMB cross-correlationdark energyw0waCDMtomographyPlanck CMB
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 reading

This paper tries to establish that the integrated Sachs–Wolfe effect—the imprint of late-time gravitational-potential decay on CMB photons—shows up in the cross-correlation between the Quaia quasar catalogue and Planck temperature maps. The central result is a 2.8σ detection with amplitude A_ISW = 1.69 ± 0.61 times the Planck ΛCDM prediction, meaning the measured signal is somewhat stronger than the standard model expects but still statistically consistent with it. The paper also argues this amplitude is stable when the CMB map, quasar bias model, sky region, multipole range, or binning scheme is changed, and that the w0waCDM dark-energy models favoured by recent BAO and weak-lensing data predict a lower signal and therefore do not explain the excess. A reader should care because ISW measurements are one of the few direct fingerprints of dark energy's effect on structure growth, and a true excess would point beyond ΛCDM.

Core claim

The paper's central claim is that the ISW cross-correlation signal is present in the Quaia × Planck data at 2.8σ significance, with best-fit amplitude A_ISW ≈ 1.69 ± 0.61 relative to the fiducial Planck ΛCDM template. Split by redshift, the low-z bin (z̄ ≈ 0.97) gives 1.19 ± 0.56, the high-z bin (z̄ ≈ 2.10) gives 2.86 ± 1.62, and a joint fit over both bins gives 1.38 ± 0.53. The w0waCDM models used in the analysis, with parameters taken from recent baryon-acoustic-oscillation and weak-lensing constraints, predict ISW spectra lower than ΛCDM by at most about 20%, and fitting them to the data does not improve χ²; in fact the data prefer an amplitude above the ΛCDM template, in the opposite dir

What carries the argument

The central object is the tomographic angular cross-power spectrum C^{Tg}_ℓ between Planck temperature and Quaia quasar overdensity maps, computed with a standard pseudo-Cℓ spherical-harmonic mode-coupling estimator on a common sky mask and fitted by a single amplitude A_ISW. The theoretical template combines an ISW kernel W_ISW(χ) ∝ H(z) [1 - f(z)]—the rate at which gravitational potentials decay with time—with a quasar kernel b(z) dN/dz, where the quasar bias is assumed to follow b(z) = b0 / D(z) with b0 = 1.26. The covariance is estimated from 2000 correlated Gaussian mock realizations of the CMB and quasar density fields, so the fit accounts for cosmic variance and shot noise. This machi

Load-bearing premise

The load-bearing assumption is the fixed quasar clustering bias, b0 = 1.26 in the model b(z) = b0 / D(z); if the true bias differs, the fitted signal amplitude shifts by the inverse factor and the dark-energy comparison changes, even though the detection significance does not.

What would settle it

Measure the actual large-scale bias of the Quaia z≈0.97 bin from its autocorrelation or from cross-correlation with CMB lensing, and compare with 1.26; if the true b0 were, say, 1.5, the central amplitude would fall to about 1.4, within 1σ of ΛCDM. A bias-independent high-redshift ISW measurement using a different tracer with precisely known bias at z≈2 would settle whether the 2.86 ± 1.62 amplitude is physical.

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

If this is right

  • If the central claim is right, the ISW effect is detected in the largest-volume quasar sample to date, providing an independent, growth-based confirmation that gravitational potentials decay at late times as ΛCDM predicts.
  • The tomographic split indicates the signal is not carried only by low redshift: the high-z bin (z̄≈2.10) yields A_ISW = 2.86 ± 1.62, consistent with previous quasar-ISW estimates, though with large uncertainty.
  • The measured amplitude exceeds ΛCDM by about 1.1σ, so the result is not evidence against ΛCDM, but it narrows the room for models, like the w0waCDM ones used here, that predict a weaker ISW signal.
  • The robustness tests—three CMB maps, an alternative bias model, hemisphere splits, and varying ℓmax and bin count—all keep A_ISW within 1σ of the baseline, supporting the interpretation that the cross-correlation is not dominated by a particular analysis choice.
  • Future wide-area surveys with higher quasar densities will reduce shot noise and can test whether the excess grows or shrinks, which the paper identifies as the path to distinguishing dark-energy models.

Where Pith is reading between the lines

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

  • A direct measurement of Quaia's quasar bias normalization at low redshift would be the fastest check: since the fitted amplitude scales as 1/b0, an upward correction to b0 would pull A_ISW toward 1 and the excess would largely dissolve; a downward correction would strengthen it.
  • The high-z bin is where the excess is most pronounced (2.86 ± 1.62) and where shot noise is largest; a dedicated wide-area sample at z≈2 with much higher tracer density could separate a genuine high-z ISW excess from a statistical outlier.
  • If the excess persists after bias and systematics are controlled, it points toward models that produce faster late-time potential decay than ΛCDM (for example higher Ωm or σ8, or w > -1), the opposite direction from the w0waCDM fits favoured by current BAO and lensing data; this would be a tension worth pursuing, though the paper does not draw that conclusion.
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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 tomographic cross-correlation analysis between the Quaia quasar catalogue and Planck 2018 CMB temperature maps, measuring the integrated Sachs-Wolfe (ISW) effect. Using a pseudo-Cℓ pipeline with 2000 mock-based covariances, the authors report a best-fit ISW amplitude A_ISW = 1.69 ± 0.61 (2.78σ) relative to the Planck ΛCDM prediction for the total quasar sample, with low-z and high-z bin amplitudes of 1.19 ± 0.56 and 2.86 ± 1.62, respectively. They also compare against two w0waCDM models favoured by recent DESI/DES data and find these models do not explain the mildly elevated amplitude. Robustness tests include alternative CMB component-separation maps, a second quasar bias model, North/South sky splits, and variations of multipole binning and ℓmax. The central claim is an ISW detection at ~2.8σ with an amplitude consistent with ΛCDM at 1.1σ, and the paper argues that current data cannot distinguish ΛCDM from the CPL models but prefer an amplitude above both.

Significance. If taken at face value, the result provides one of the most extensive tomographic ISW measurements to date, using the Quaia catalogue's large sky area and redshift depth. The analysis is methodologically transparent: it uses the public NaMaster pseudo-Cℓ estimator, a covariance from 2000 correlated Gaussian mocks with Hartlap correction, and external cosmological parameters from Planck and DESI/DES, avoiding circular use of the ISW amplitude. The robustness tests, especially the use of NILC and SEVEM CMB maps and the alternative bias model, strengthen confidence in the amplitude stability. The paper also gives a useful comparison with w0waCDM models motivated by recent dark-energy hints. However, the headline significance is scale-dependent—dropping to 2.1σ when ℓmax is restricted to the linear regime—and the fixed quasar bias normalization adds unquantified systematic uncertainty to the amplitude. These issues must be addressed before the detection claim is fully supported.

major comments (3)
  1. [§3.1, §3.3, Fig. 4] The headline detection significance of 2.8σ (abstract, §3.1) is not stable under the choice of ℓmax: restricting to ℓmax=100 with 5 bins gives A_ISW=1.30±0.61, i.e. S/N=2.13σ, while the fiducial ℓmax=300 yields 2.78σ. The paper states in §3.3 that results are 'robust', but this robustness applies to the amplitude, not to the significance. Since the central claim is a detection at 2.8σ, this scale dependence is load-bearing. Please report the linear-regime significance as a primary result, or provide a quantitative justification for including multipoles 100–300 (e.g., validation of the template and covariance on those scales) rather than relying on a 1σ amplitude consistency.
  2. [§2.2, Eq. (2); §3.3] The quasar bias normalization b0=1.26 is fixed from Piccirilli et al. without propagating its uncertainty. The ISW cross-spectrum template is proportional to b(z), so A_ISW scales inversely with b0. The alternative bias model of Laurent et al. shifts A_ISW from 1.69 to 2.02 (§3.3), illustrating the sensitivity. Since the paper uses A_ISW to assess dark-energy models, the error on A_ISW should include the bias uncertainty. Please marginalize over b0 with a prior informed by Piccirilli et al., or at least quote a systematic error from the allowed b0 range. Without this, the reported 1σ error is underestimated.
  3. [§3.3, Fig. 3] The increase in significance from ℓmax=100 to ℓmax=300 appears driven by multipoles 100–300, where the ISW template is small relative to the error bars and where the paper notes 'an outlier data point ... at ℓ≈200' even for the total sample. The text dismisses this as a statistical fluctuation, but no explicit test is shown—e.g., removing that bin from the fit, comparing with a map without the outlier, or examining known foreground residuals (CIB, tSZ) on those scales. Given that this outlier contributes to the 2.8σ claim, its nature should be tested rather than assumed, and the resulting significance change should be reported.
minor comments (4)
  1. [§4] Typo: 'comsic maps' should be 'cosmic maps'.
  2. [Fig. 2] The y-axis label 'Custume Normalized dN/dz' appears to be a typo; should likely be 'Custom Normalized dN/dz' or simply 'Normalized dN/dz'.
  3. [§2.5] The description of the mask construction is clear, but it would help to state the total unmasked sky fraction for the joint masks used in the fiducial analysis, as this affects cosmic variance and the interpretation of the significance.
  4. [§3.2] The wCDM model with w=−0.65 is mentioned as 'ad-hoc' and likely ruled out by other constraints; consider removing it or explicitly labeling it as an illustrative exercise, since it could be mistaken for a viable scenario.

Circularity Check

0 steps flagged

No load-bearing circularity: the ISW amplitude is a fitted output against externally computed theory templates; self-citations are methodological and peripheral.

full rationale

The central result, A_ISW = 1.69 +/- 0.61, is obtained by fitting the measured binned cross-spectrum d_b to a theoretical template t_b via a chi^2 minimization (Eqs. 9-10). The template is computed with pyCCL/CAMB using external Planck 2018 LambdaCDM parameters and external DES/DESI CPL parameters, not from the Quaia data. Thus the amplitude is a fitted output, not an input, and no self-definitional circularity is present. The mock catalogues used for the covariance are generated from the theory spectra, including the LambdaCDM cross-spectrum; this is standard practice for covariance estimation and does not force the measured amplitude, since the data vector is independent of the mocks. The fixed bias b0 = 1.26 from Piccirilli et al. (2024) is an external input and is robustly tested against an alternative bias model; any bias uncertainty affects the amplitude but does not make the derivation circular. The only self-citations are methodological or peripheral: Bermejo-Climent et al. (2026) for the power-law correction added to the galaxy auto-spectrum in mocks, and Ghodsi Yengejeh et al. (2026) for an exploratory remark about quintessence models. Neither supports the ISW detection claim itself. The paper also transparently flags outlier data points at ell ~ 200 and the reduced significance (2.13 sigma) at ell_max = 100; this is a robustness concern, not circularity. No specific reduction of a prediction to an input can be exhibited, so there is no significant circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 9 axioms · 0 invented entities

The paper's model inputs are standard: Planck 2018 ΛCDM, CPL parameters from DES/DESI, and a quasar bias calibration from the literature. The only quantities fitted to the data are the A_ISW amplitudes, which are the measured outputs. The covariance mocks add a power-law enhancement to the quasar auto-spectrum as a nuisance, following prior work, but this does not enter the central amplitude estimate.

free parameters (5)
  • ISW amplitude A_ISW (total sample) = 1.69 ± 0.61
    Fitted via χ² minimization (Eq. 9/10) to the binned Quaia×Planck cross-spectrum; central result.
  • A_ISW (low-z bin) = 1.19 ± 0.56
    Per-bin amplitude for the z~0.97 sample.
  • A_ISW (high-z bin) = 2.86 ± 1.62
    Per-bin amplitude for the z~2.10 sample.
  • A_ISW (joint fit) = 1.38 ± 0.53
    Joint fit to concatenated low-z and high-z data vectors (12 bins).
  • quasar bias normalization b0 = 1.26
    Adopted from Piccirilli et al. (2024) and fixed; the template is proportional to b(z), so A_ISW scales as 1/b0; its uncertainty is not propagated. An alternative bias model shifts A_ISW to 2.02.
axioms (9)
  • domain assumption Flat ΛCDM with Planck 2018 best-fit parameters as the fiducial cosmology.
    Used to compute the theory ISW template and mocks; if the true cosmology differs, the A_ISW=1 reference shifts. Invoked in Section 2.3.
  • domain assumption CPL parameterization w(a)=w0+wa(1−a) with DESI/DES best-fit parameters (w0=−0.84, wa=−0.53 for All DES+DESI BAO; w0=−0.84, wa=−0.44 for All DES).
    External constraints adopted as given; the ISW kernels for these models are compared; Section 2.3.
  • domain assumption Quasar linear bias evolves as b_QSO(z)=b0/D(z) with b0=1.26.
    Standard bias evolution ansatz; the cross-correlation template scales with b(z); Section 2.2.
  • domain assumption Magnification bias s=0.4 exactly, so the lensing-magnification contribution cancels.
    The measured s=0.404±0.004 is consistent with 0.4; if s differs, a small magnification term enters the kernel; Section 2.2.
  • domain assumption Redshift-space distortions are negligible for the ISW cross-correlation.
    The RSD term is not included in the number-count kernel; Section 2.3.
  • domain assumption Non-linear Rees-Sciama contribution is negligible at ℓ≤300.
    The RS signal is ~10% of the linear ISW in auto-correlation at ℓ≥200 and further suppressed in cross-correlation; the ℓmax=100 check supports this; Section 2.3/3.3.
  • standard math Limber approximation is valid for these cross-spectra.
    Used to compute C^{XY}_ℓ (Eq. 4); standard for these broad kernels.
  • domain assumption Gaussian mocks with added Poisson shot noise and Planck noise accurately estimate the covariance.
    The covariance is estimated from 2000 Gaussian realizations generated from the theory spectra (plus an added power-law in C_gg to match data); Section 2.4/2.6.
  • domain assumption The ISW signal shape is fixed, with only a scale-independent amplitude free.
    A single amplitude is fit to the template; if the true ISW shape differs (e.g., modified growth), the interpretation of A_ISW changes; Section 2.6.

reviewed 2026-08-01 · how reviews work

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Cite this review

Pith. "Pith review of Probing dark energy evolution with Quaia quasars through the integrated Sachs-Wolfe effect." pith.science (2026). https://pith.science/paper/SYMLK2LL

@misc{pith2026260722461,
  author       = {Pith},
  title        = {Pith review of: Probing dark energy evolution with Quaia quasars through the integrated Sachs-Wolfe effect},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SYMLK2LL}},
  note         = {Machine review of arXiv:2607.22461}
}
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abstract

The Integrated Sachs--Wolfe (ISW) effect probes the late-time evolution of gravitational potentials and provides a complementary test of the nature of dark energy. We investigate whether the redshift evolution of the ISW effect can provide new constraints on the time evolution of dark energy. We consider theoretical predictions for the standard $\Lambda$CDM cosmology and alternative $w_0w_a$CDM models favoured by recent DESI BAO and DES Y6 constraints. We perform a tomographic cross-correlation analysis of the {\it Quaia} quasar catalogue and \textit{Planck} CMB temperature maps to measure the ISW signal over a broad redshift range, spanning about $(10h^{-1}~\mathrm{Gpc})^3$ comoving volume. We assess the robustness of the inferred ISW amplitude against variations in sky coverage, multipole range, and tomographic binning. We detect the ISW effect at a significance of $2.8 \, \sigma$, corresponding to an amplitude of $A_{\rm ISW}\simeq1.69\pm0.61$ relative to the \textit{Planck} $\Lambda$CDM prediction. The inferred signal remains stable against various analysis choices, including various CMB maps (SMICA, NILC, SEVEM), different choices of $\ell_{\rm max}$ and the number of multipole bins, and an alternative quasar bias model. The measured ISW amplitude is moderately stronger than predicted by the fiducial $\Lambda$CDM cosmology, and the alternative $w_0w_a$CDM models do not account for this discrepancy. Future tomographic ISW measurements with improved quasar catalogues from {\it Gaia} and forthcoming wide-area galaxy surveys such as {\it Euclid} and DESI will help clarify the origin of this difference.

Figures

Figures reproduced from arXiv: 2607.22461 by A. Kov\'acs, I. Csabai, I. Szapudi, J. R. Bermejo-Climent, M. Ghodsi Yengejeh.

Figure 1
Figure 1. Figure 1: Orthographic (half-sky) projections of the two maps entering our cross-correlations, left) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top panel: Normalised Quaia redshift distributions (dN/dz) for Bin 1 (blue), Bin 2 (green), and the total sam￾ple (purple), together with the ISW kernel per unit redshift (WISW(z)/H(z)) computed with pyCCL for our three theoreti￾cal models: ΛCDM with the Planck 2018 best-fit parameters (solid), CPL with the All DES + DESI BAO best-fit parameters (dashed), and CPL with the All DES best-fit parameters (dotte… view at source ↗
Figure 3
Figure 3. Figure 3: Top row: Binned angular cross-power spectra [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The best-fit amplitude AISW for all analysis setups. Mark￾ers show central values with 1σ error bars, and numbers below show detection significance. The top three markers are our base￾line SMICA × Quaia results, separated by a dashed line from robustness tests using alternative component-separation maps (NILC, SEVEM), a different bias model, North-South hemi￾sphere splits, and different choices for binning… view at source ↗

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Works this paper leans on

46 extracted references · 2 linked inside Pith

  1. [1]

    Abbott, T. M. C. et al. 2026, arXiv e-prints, arXiv:2605.27221 Abdul Karim, M., Aguilar, J., Ahlen, S., et al. 2025, Phys. Rev. D, 112, 083515

    Pith/arXiv arXiv 2026

  2. [2]

    G., Aguilar, J., Ahlen, S., et al

    Adame, A. G., Aguilar, J., Ahlen, S., et al. 2025, JCAP, 02, 021

    2025

  3. [3]

    2004, Physical Review D, 70, 083536

    Afshordi, N. 2004, Physical Review D, 70, 083536

    2004

  4. [4]

    2023, JCAP, 2023, 043

    Alonso, D., Fabbian, G., Storey-Fisher, K., et al. 2023, JCAP, 2023, 043

    2023

  5. [5]

    2025, The Open Journal of As- trophysics, 8, 42

    Alonso, D., Hetmantsev, O., Fabbian, G., et al. 2025, The Open Journal of As- trophysics, 8, 42

    2025

  6. [6]

    2019, Mon

    Alonso, D., Sanchez, J., & Slosar, A. 2019, Mon. Not. Roy. Astron. Soc., 484, 4127

    2019

  7. [7]

    2026, arXiv e-prints, arXiv:2602.02363

    Andrews, A., Loureiro, A., Jasche, J., et al. 2026, arXiv e-prints, arXiv:2602.02363

    arXiv 2026

  8. [8]

    P., et al

    Arsenov, N., Kovacs, A., Sar, M. P., et al. 2026, Astron. Astrophys., 706, A362

    2026

  9. [9]

    2022, Monthly Notices of the Royal Astronomical Society, 517, 3785–3803

    Bahr-Kalus, B., Parkinson, D., Asorey, J., et al. 2022, Monthly Notices of the Royal Astronomical Society, 517, 3785–3803

    2022

  10. [10]

    R., Hernández-Monteagudo, C., Crespo-Pérez, A., et al

    Bermejo-Climent, J. R., Hernández-Monteagudo, C., Crespo-Pérez, A., et al. 2026, A&A, 710, A360

    2026

  11. [11]

    & Crittenden, R

    Boughn, S. & Crittenden, R. 2004, Nature, 427, 45 Cabré, A., Fosalba, P., Gaztañaga, E., & Manera, M. 2007, MNRAS, 381, 1347

    2004

  12. [12]

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

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

    2013

  13. [13]

    2009, MNRAS, 396, 772

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

    2009

  14. [14]

    Cai, Y .-C., Cole, S., Jenkins, A., & Frenk, C. S. 2010, MNRAS, 407, 201

    2010

  15. [15]

    & Polarski, D

    Chevallier, M. & Polarski, D. 2001, Int. J. Mod. Phys. D, 10, 213

    2001

  16. [16]

    E., Alonso, D., Krause, E., et al

    Chisari, N. E., Alonso, D., Krause, E., et al. 2019, The Astrophysical Journal Supplement Series, 242, 2

    2019

  17. [17]

    2026, Journal of Cos- mology and Astroparticle Physics, 2026, 056

    Fabbian, G., Alonso, D., Storey-Fisher, K., & Cornish, T. 2026, Journal of Cos- mology and Astroparticle Physics, 2026, 056

    2026

  18. [18]

    D., & Spergel, D

    Ferraro, S., Sherwin, B. D., & Spergel, D. N. 2015, Phys. Rev. D, 91, 083533 Ghodsi Yengejeh, M., Kovács, A., Szapudi, I., et al. 2026, Astron. Astrophys., 709, A101

    2015

  19. [19]

    G., & et al

    Giannantonio, T., Scranton, R., Crittenden, R. G., & et al. 2008, Phys. Rev. D, 77, 123520

    2008

  20. [20]

    M., Hivon, E., Banday, A

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

    2005

  21. [21]

    R., Neyrinck, M

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

    2008

  22. [22]

    & Challinor, A

    Gratton, S. & Challinor, A. 2020, Monthly Notices of the Royal Astronomical Society, 499, 3410–3416

    2020

  23. [23]

    K., Lambas, D

    Hansen, F. K., Lambas, D. G., Ruiz, A. N., et al. 2025, arXiv e-prints, arXiv:2506.08832

    Pith/arXiv arXiv 2025

  24. [24]

    2007, A&A, 464, 399 Hernández-Monteagudo, C

    Hartlap, J., Simon, P., & Schneider, P. 2007, A&A, 464, 399 Hernández-Monteagudo, C. & Smith, R. E. 2013, MNRAS, 435, 1094

    2007

  25. [25]

    M., Netterfield, C

    Hivon, E., Gorski, K. M., Netterfield, C. B., et al. 2002, ApJ, 567, 2–17

    2002

  26. [26]

    2008, Physical Review D, 78, 043519

    Ho, S., Hirata, C., Padmanabhan, N., Seljak, U., & Bahcall, N. 2008, Physical Review D, 78, 043519

    2008

  27. [27]

    2015, MNRAS, 446, 1321 Héder, M., Rigó, E., Medgyesi, D., et al

    Hotchkiss, S., Nadathur, S., Gottlöber, S., et al. 2015, MNRAS, 446, 1321 Héder, M., Rigó, E., Medgyesi, D., et al. 2022, Információs Társadalom, 22, 128 Ili´c, S., Langer, M., & Douspis, M. 2013, A&A, 556, A51 Kovács, A., Beck, R., Smith, A., et al. 2022a, MNRAS, 513, 15 Kovács, A., Jeffrey, N., Gatti, M., et al. 2022b, MNRAS, 510, 216 Kovács, A., Sánche...

    2015

  28. [28]

    & Ferraro, S

    Krolewski, A. & Ferraro, S. 2022, JCAP, 04, 033

    2022

  29. [29]

    L., et al

    Laurent, P., Eftekharzadeh, S., Goff, J.-M. L., et al. 2017, JCAP, 2017, 017

    2017

  30. [30]

    & Challinor, A

    Lewis, A. & Challinor, A. 2011, CAMB: Code for Anisotropies in the Microwave

    2011

  31. [31]

    Linder, E. V . 2003, Phys. Rev. Lett., 90, 091301

    2003

  32. [32]

    & Crittenden, R

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

    2016

  33. [33]

    & Hotchkiss, S

    Nadathur, S. & Hotchkiss, S. 2015, MNRAS, 454, 889

    2015

  34. [34]

    2017, MNRAS, 472, L65

    Naidoo, K., Benoit-Lévy, A., & Lahav, O. 2017, MNRAS, 472, L65

    2017

  35. [35]

    2024, JCAP, 012 Planck Collaboration

    Piccirilli, G., Fabbian, G., Alonso, D., et al. 2024, JCAP, 012 Planck Collaboration. 2016, A&A, 594, A21 Planck Collaboration, Aghanim, N., Akrami, Y ., et al. 2020, A&A, 641, A6

    2024

  36. [36]

    Popovic, B. et al. 2026, Mon. Not. Roy. Astron. Soc., 548, stag632

    2026

  37. [37]

    Rees, M. J. & Sciama, D. W. 1968, Nature, 217, 511

    1968

  38. [38]

    G., Filippenko, A

    Riess, A. G., Filippenko, A. V . Challis, P., & et al. 1998, AJ, 116, 1009

    1998

  39. [39]

    Rudnick, L., Brown, S., & Williams, L. R. 2007, ApJ, 671, 40

    2007

  40. [40]

    Sachs, R. K. & Wolfe, A. M. 1967, ApJL, 147, 73

    1967

  41. [41]

    F., Meisner, A

    Schlafly, E. F., Meisner, A. M., & Green, G. M. 2019, ApJ Supplement Series, 240, 30 Stölzner, B., Cuoco, A., Lesgourgues, J., & Bilicki, M. 2018, Phys. Rev. D, 97, 063506

    2019

  42. [42]

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

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

    2024

  43. [43]

    R., et al

    Szapudi, I., Kovács, A., Granett, B. R., et al. 2015, MNRAS, 450, 288

    2015

  44. [44]

    2012, ApJ, 761, 152

    Takahashi, R., Sato, M., Nishimichi, T., et al. 2012, ApJ, 761, 152

    2012

  45. [45]

    2009, JCAP, 09, 003

    Xia, J.-Q., Viel, M., Baccigalupi, C., & Matarrese, S. 2009, JCAP, 09, 003

    2009

  46. [46]

    2019, Journal of Open Source Software, 4, 1298 Article number, page 8

    Zonca, A., Singer, L., Lenz, D., et al. 2019, Journal of Open Source Software, 4, 1298 Article number, page 8

    2019

This paper was first reviewed by deepseek-v4-flash on August 1, 2026.