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REVIEW 4 major objections 4 minor 108 references

The imprint of cosmic voids from the DESI Legacy Survey DR9 LRGs in the Planck 2018 lensing map through spectroscopically calibrated mocks

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Cross-correlating 140,712 cosmic voids from the DESI Legacy Survey DR9 LRG sample with the Planck 2018 CMB lensing map yields a lensing amplitude Aκ = 1.016 ± 0.054, in full agreement with ΛCDM predictions once the Buzzard mocks are…

desk verdict A serious, well-calibrated void-lensing measurement whose central A_kappa ~ 1 claim is probably right, but the headline 14 sigma and 17 sigma significances rest on a doubtful chi-square formula and a post-hoc bin choice. read the letter →

arxiv 2412.02761 v1 pith:NC2PFMAR submitted 2024-12-03 astro-ph.CO

S. Sartori , P. Vielzeuf , S. Escoffier , M. C. Cousinou , A. Kovács , J. DeRose , S. Ahlen , D. Bianchi
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D. Brooks E. Burtin T. Claybaugh A. de la Macorra J. E. Forero-Romero J. Garcia-Bellido S. Gontcho A Gontcho G. Gutierrez K. Honscheid R. Kehoe D. Kirkby T. Kisner M. Landriau M. E. Levi A. Meisner R. Miquel J. Moustakas J. A. Newman N. Palanque-Delabrouille I. Pérez-Ràfols F. Prada G. Rossi E. Sanchez D. Sprayberry G. Tarlé B. A. Weaver
This is my paper · ORCID
classification astro-ph.CO
keywords cosmicvoidsCMBlensingDESILegacySurveyDR9luminousredgalaxiesvoid-in-voidvoid-in-cloudBuzzardmockslensing-is-lowtension
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

This paper aims to settle the "lensing-is-low" tension in void cosmology: several earlier studies found that the CMB lensing signal around cosmic voids was weaker than ΛCDM simulations predicted, by up to about 3σ. The authors argue that the tension was an artifact of mismatched mock catalogs, and that once the simulated galaxy samples are calibrated to match the photometric-redshift errors and sparseness of the real DESI Legacy Survey DR9 LRG sample, the observed void lensing signal agrees with ΛCDM predictions everywhere. Using 140,712 3D voids and the Planck 2018 convergence map, they measure a lensing amplitude Aκ = 1.016 ± 0.054 (14σ detection) for the full sample, and even higher significance when splitting voids into void-in-void and void-in-cloud populations by λv. The result matters because it removes a notable observational challenge to ΛCDM and demonstrates that systematic matching of mocks to data is decisive for void lensing tests.

What carries the argument

The analysis is carried by three coupled elements: a 3D void catalog built with the REVOLVER/ZOBOV watershed algorithm; the λv parameter, defined as λv = δ̄v (Rv / 1 h⁻¹ Mpc)^1.2, which separates void-in-voids (negative λv, strongly underdense) from void-in-clouds (positive λv, embedded in overdense environments); and a template-fitting scheme in which the observed stacked convergence profile is compared with a ΛCDM template from four Buzzard mock realizations. The mocks are first calibrated: photometric redshifts of mock galaxies are resampled so that the mock redshift-error CDF matches the observed one derived from about one million DESI spectra, and the mock galaxy samples are subsampled to match the observed sparseness (mean galaxy separation) in the North and South caps separately. The stacked signal is measured on a Planck 2018 convergence map smoothed with a 0.5° Gaussian filter, using patches of radius 5 times the void radius, with errors from 1000 random realizations of the CMB lensing field and a Hartlap-corrected covariance.

What would settle it

Recompute Aκ using voids identified directly from spectroscopic redshifts (or from a fully spectroscopic survey) and compare with the photo-z-based measurement; a significant shift in Aκ would indicate the photo-z calibration does not fully capture the void population. Alternatively, generate mock templates from an independent simulation suite without the photo-z CDF remapping and check whether Aκ deviates from unity, which would show that the calibration is doing the work. A third check: artificially amplify the residual sparseness mismatch at z < 0.5 and z > 0.8 and see whether Aκ moves by more than the current 5% uncertainty.

Watch

Extended reading notes

Core claim

The central claim is that the cross-correlation between cosmic voids and CMB lensing in the observed universe is fully consistent with the ΛCDM prediction, once the simulated template is built from mocks whose photometric redshift error distribution and galaxy sparseness are calibrated against the actual DESI Legacy Survey LRG sample using more than one million DESI spectra. In the full-sky sample of 140,712 voids between 0.35 < z < 0.95, the best-fit lensing amplitude is Aκ = 1.016 ± 0.054, a 14σ detection; separating voids into negative-λv (void-in-void) and positive-λv (void-in-cloud) populations yields Aκ = 0.944 ± 0.064 and Aκ = 0.975 ± 0.060, respectively, with signal-to-noise ratios of about 17. The same agreement holds in the North and South Galactic Caps separately (Aκ = 1.088 ± 0.081 and Aκ = 0.936 ± 0.087) and across all four redshift bins. The authors interpret the previously reported "lensing-is-low" tension as a systematic effect: uncalibrated mocks produce void populations with different lensing properties, and matching sparseness and redshift errors removes the discrepancy.

Load-bearing premise

The analysis assumes that the Buzzard mocks, after calibration, are an unbiased template for the lensing signal of the true void population, in particular that the photometric-redshift error CDF measured from about one million DESI spectra represents the full 10.4 million LRG sample, and that residual sparseness differences below 5% at z < 0.5 and z > 0.8 have negligible impact on void identification and lensing amplitude.

Editorial extensions

If this is right

  • If correct, the "lensing-is-low" tension in void-CMB lensing is resolved as a systematic of mock construction, not evidence against ΛCDM.
  • Void lensing measurements at 14-17σ significance become competitive probes of the matter distribution, and the λv-split populations give independent high-S/N channels.
  • Future void lensing analyses must match photometric redshift errors and sparseness between mocks and data; otherwise they risk producing artificial tensions.
  • The tomographic result, with consistent Aκ across four redshift bins, strengthens the case that the void lensing kernel evolves as ΛCDM predicts.

Reading between the lines

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

  • A direct extension would be to repeat the calibration procedure on an independent mock suite, or with voids identified from spectroscopic redshifts, to test whether Aκ ≈ 1 is robust to the choice of calibration target; the paper itself notes residual sparseness differences below 5% at the redshift edges.
  • The same calibration logic could be applied to other large-scale structure lensing probes, such as clusters or cosmic filaments, where similar "low lensing" anomalies have been reported; those tensions may also shrink once mock selection effects are matched.
  • The λv-based population split, which the paper shows increases S/N, could be optimized further by fine-tuning the bin edges to push detection significance beyond 17σ with current data.
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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. This paper measures the stacked imprint of cosmic voids from the DESI Legacy Survey DR9 LRG sample on the Planck 2018 CMB lensing convergence map, and compares it to a ΛCDM template built from four Buzzard mock realizations that are calibrated to the observed galaxy clustering, photometric redshift errors, and sparseness. The amplitude of the observed signal relative to the template is fitted as a free parameter Aκ. The authors report Aκ = 1.016 ± 0.054 for the full void sample (S/N = 14), and consistent values for subpopulations split by the λv void parameter, concluding that the previously reported 'lensing-is-low' tension is eliminated when the mocks are properly calibrated.

Significance. If correct, this result would resolve a current tension in void-CMB lensing studies and would demonstrate that the discrepancy was driven by mock galaxy catalogs that did not reproduce the photometric and sparseness properties of the real data. The paper makes a strong methodological contribution by showing quantitative improvements from matching photo-z error CDFs and sparse-sampling the mocks to the survey. The use of four independent mock realizations and the public data availability are positive features. However, the central quantitative claims hinge on the template-fitting statistic and on the treatment of the data-driven λv bin choice.

major comments (4)
  1. [§3.4, Eq. (15)] The chi-square statistic used for the template fit is not the chi-square of the residual. For independent Legacy and Buzzard measurements, the residual d(A) = x^L - A x^B has covariance C^L + A^2 C^B, so the correct statistic is d(A)^T (C^L + A^2 C^B)^{-1} d(A). Equation (15) instead uses (C^L)^{-1} + A^2 (C^B)^{-1}, which is the sum of precisions and is not the inverse of the residual covariance. The limiting case C^B → 0 makes the problem clear: Eq. (15) diverges, whereas the correct statistic reduces to the data-only chi-square. Because every value of Aκ, σ_Aκ, and S/N in Tables 2–4 is obtained from Eq. (15), the reported 14σ detection and 17σ sub-population significances are not presently supported. The authors should repeat the analysis with the correct likelihood, or provide a formal justification for their weighting (e.g., if one of the covariance matrices is negligible, this should be demonstrated bin-by-bin).
  2. [§3.2.1 and §5] The λv bin boundaries (λv = -5 and +5) are described as chosen to approximately maximize the signal-to-noise ratio. If these boundaries were selected after inspecting the observed data, the quoted S/N values for the void-in-void and void-in-cloud samples (16.94 and 17.02) are optimistic and the corresponding '17σ' claim in the abstract is not a valid detection significance. The authors should either demonstrate that the boundaries were fixed a priori based on previous literature (e.g., Raghunathan et al. 2020) or quantify the trials factor associated with scanning over bin boundaries. The full-sample result is not affected by this concern, but the sub-population significance claims are.
  3. [§3.4, Eq. (17)] The detection significance S/N is defined as the maximum of M_j/σ_j over the 25 radial bins. Since the bins are correlated and the maximum over a set of noise realizations is biased high, the quoted 14σ and 17σ values overstate the significance of the detection unless a trials correction is applied. The authors should quote the amplitude significance from the template fit (Aκ/σ_Aκ) as the primary detection significance, or provide an effective number of independent bins.
  4. [§3.1.2] The statement that residual sparseness differences below 5% (at z<0.5 and z>0.8) have 'almost negligible' impact on void identification is not demonstrated. Given that the tomographic analysis in Section 4.2 reports agreement with ΛCDM in these very redshift bins, the authors should provide a quantitative test, e.g., constructing additional mock realizations with matched sparseness in those ranges or comparing void property distributions in the affected bins separately, to show that the residual mismatch does not bias Aκ.
minor comments (4)
  1. [§4.2 vs. Table 3] The uncertainty for the negative-λv bin is given as 0.060 in the text but 0.064 in Table 3 and the abstract; the authors should correct the inconsistency.
  2. [§3.4, Eq. (16)] The sentence about the Hartlap correction says it decreases the covariance value by ~2.6%; the factor in Eq. (16) actually multiplies the inverse covariance, so it increases the effective covariance. Please rephrase to avoid confusion.
  3. [§3.4, Eq. (14)] The expression for the mock covariance in Eq. (14) uses (1/N) times the average internal covariance; if this is intended to be the covariance of the mean template, a factor of 1/N may be missing, and the authors should clarify the normalization.
  4. [General terminology] The use of 'full-sky' to refer to the combined North+South survey footprint is misleading, since only ~19,500 deg² of the sky is covered; consider 'full-survey' or 'combined' instead.

Circularity Check

1 steps flagged · score 4.0 of 10

Core A_kappa measurement is an independent template fit; the 17-sigma subpopulation significances are selected on the same S/N objective used to choose the lambda_v bins.

  1. fitted input called prediction [Sec. 3.2.1 (void catalogs); Sec. 4.2 and Table 3 (full-sky results)]
    "These specific λ_v-binning values were chosen to approximately maximize the signal-to-noise ratio. ... we measured Aκ = 0.944±0.060 (S/N = 16.94) for the negative λ_v bin, Aκ = 0.975±0.060 (S/N = 17.02) for the positive λ_v bin."

    The λ_v bin edges are selected to maximize S/N, and the same S/N statistic is then reported as the headline detection significance for the void-in-void and void-in-cloud subsamples. Choosing the binning that optimizes S/N and then quoting the optimized S/N as an independent discovery significance is a selection effect: the reported 16.94 and 17.02 values are the outcome of an optimization, not a prediction made before the bin choice. The A_kappa amplitudes in these bins remain genuine comparisons, so this circularity is partial and does not by construction force A_kappa = 1.

full rationale

The central A_kappa measurement is not circular. The Buzzard mock template is generated from ΛCDM N-body lightcone simulations, with calibration applied to photometric redshift errors and galaxy sparseness to match the DESI LRG sample; the Planck lensing data are not used in that calibration. Fitting A_kappa = kappa_Legacy / kappa_Buzzard is therefore an independent amplitude comparison, and the reported A_kappa ≈ 1 is a real consistency result rather than an input recovered by construction. The one circular element is the subpopulation significance claim: the λ_v bin boundaries are explicitly chosen to approximately maximize S/N, and the abstract's 17σ values for void-in-void and void-in-cloud are quoted from those same optimized bins without a trials correction. This affects the significance headline but does not force the cosmological amplitude. The skeptic's Eq. (15) concern is a statistical-error issue rather than a circularity: the chi-square form is adopted from a self-citation (Vielzeuf et al. 2021, with overlapping authors) and carries all quoted uncertainties, but a wrong or imported covariance formula does not make the measurement equivalent to its inputs by definition. Overall, the main cosmological claim has independent content, with a partial circularity in the S/N-maximized subpopulation claims.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The ledger lists the externally assumed inputs. The main items are the Buzzard mock cosmology, the representativeness of the spectroscopic subsample, the negligible-impact claim for residual sparseness mismatch, the Born-approximation lensing model, and the algorithmic void definition. The only notable data-driven free parameter is the λ_v binning, chosen post hoc to maximize S/N. No new physical entities are introduced; λ_v is adopted from Nadathur et al. (2017).

free parameters (1)
  • λ_v bin edges = -5 and 5 (dimensionless)
    The void sample is split into void-in-void, zero-λ_v, and void-in-cloud populations using λ_v thresholds of -5 and 5. Sec. 3.2.1 states these were chosen to approximately maximize the signal-to-noise ratio, so the subpopulation significances (17σ) are optimized selections rather than pre-registered splits.
assumptions (5)
  • domain assumption The Buzzard mock lightcones with Ωm=0.286, σ8=0.82 provide an accurate ΛCDM template for the void lensing signal after calibration.
    Sec. 2.3 and Sec. 3.1: the template cosmology is fixed to the Buzzard values; the paper's 'agreement with ΛCDM' is actually agreement with this specific mock cosmology.
  • domain assumption The CDF of photo-z errors measured from about one million DESI spectroscopic redshifts is representative of the full 10.4 million LRG sample.
    Sec. 3.1.1: the calibration applies the observed z_err distribution to mock galaxies; if the spec-z subsample is not representative, the corrected mocks mismatch the true galaxy sample.
  • domain assumption Residual sparseness differences below 5% (for z<0.5 and z>0.8) have negligible impact on the void lensing template.
    Sec. 3.1.2: the paper asserts this without a quantitative propagation of the 5% density mismatch into the Aκ prediction.
  • domain assumption The Born approximation and the Poisson equation with the mean density (Eqs. 3-7) describe CMB lensing by voids at the required accuracy.
    Sec. 2.2: these are standard, but they are assumptions about the lensing physics; post-Born corrections are not quantified.
  • domain assumption REVOLVER/ZOBOV void identification with the 20% ridge merging threshold yields a void population whose lensing signal is the relevant observable.
    Sec. 3.2: the void definition is algorithmic; different void finders produce different lensing amplitudes, as acknowledged by the tension literature.

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Cite this review

Pith. "Pith review of The imprint of cosmic voids from the DESI Legacy Survey DR9 LRGs in the Planck 2018 lensing map through spectroscopically calibrated mocks." pith.science (2026). https://pith.science/paper/NC2PFMAR

@misc{pith2026241202761,
  author       = {Pith},
  title        = {Pith review of: The imprint of cosmic voids from the DESI Legacy Survey DR9 LRGs in the Planck 2018 lensing map through spectroscopically calibrated mocks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NC2PFMAR}},
  note         = {Machine review of arXiv:2412.02761}
}
abstract

The cross-correlation of cosmic voids with the lensing convergence ($\kappa$) map of the Cosmic Microwave Background (CMB) fluctuations provides a powerful tool to refine our understanding of the cosmological model. However, several studies have reported a moderate tension between the lensing imprint of cosmic voids on the observed CMB and the simulated $\mathrm{\Lambda}$CDM signal. To address this "lensing-is-low" tension and to obtain new, precise measurements, we exploit the large DESI Legacy Survey Luminous Red Galaxy (LRG) dataset, covering approximately 19,500 $\deg^2$ of the sky and including about 10 million LRGs at $z < 1.05$. Our $\mathrm{\Lambda}$CDM template was created using the Buzzard mocks, which we specifically calibrated to match the clustering properties of the observed galaxy sample by exploiting more than one million DESI spectra. We identified our catalogs of 3D voids in the range $0.35 < z < 0.95$, dividing the sample into bins according to the redshift and $\lambda_\mathrm{v}$ values of the voids. We report a 14$\sigma$ detection of the lensing signal, with $A_\kappa = 1.016 \pm 0.054$, which increases to 17$\sigma$ when considering the void-in-void ($A_\kappa = 0.944 \pm 0.064$) and the void-in-cloud ($A_\kappa = 0.975 \pm 0.060$) populations individually, the highest detection significance for studies of this kind. We observe a full agreement between the observations and $\mathrm{\Lambda}$CDM predictions across all redshift bins, sky regions, and void populations considered. In addition to these findings, our analysis highlights the importance of matching sparseness and redshift error distributions between mocks and observations, as well as the role of $\lambda_\mathrm{v}$ in enhancing the signal-to-noise ratio.

Figures

Figures reproduced from arXiv: 2412.02761 by the authors.

Figure 1
Figure 1. The different footprints of the MzLS+BASS, DECaLS, and DES surveys composing the DESI Legacy Survey, covering a total observed sky area of 19, 573 deg2 . The selected sample is integrated with 1,005,750 spectro￾scopic redshifts from DESI, in particular from the first phase of Survey Validation (SV1), the one-percent survey (SV3; covering 1% of the final area) and the first two months of the Main Survey. 2.2. CMB con… view at source ↗
Figure 2
Figure 2. Planck CMB lensing map, smoothed with a Gaussian filter of FWHM=0.5 ◦ . The DESI Legacy Survey footprint is overlaid, indicating the region where voids are identified and cross-correlations are performed. The footprint is divided into North and South regions, corresponding to the North and South Galactic Caps, respectively. Article number, page 3 of 19 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Mean Galaxy Separation (MGS) redshift evolution observed in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (10 more)
Figure 3
Figure 3. Figure 3: Redshift error distributions for the observed and one simulated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]
Figure 5
Figure 5. Figure 5: Mean Galaxy Separation (MGS) redshift evolution observed in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Probability function for the number of voids as a function of redshift for the full-sky sample, illustrating the e [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Contours in the rv−δ¯ v space for the full observed (left) and simu￾lated (right) void samples. The voids are divided into three populations according to their λv values, following the binning strategy described in Sec. 3.2.1. It can be seen that the λv subdivision is …
Figure 8
Figure 8. Figure 8: Probability distributions for rv (first column), δ¯ v (second column), and λv (third column) for voids identified in the calibrated Buzzard mocks (purple) and in the Legacy Survey (Orange). The void samples are subdivided into four equispaced redshift bins with dz = 0.…
Figure 9
Figure 9. Figure 9: Theoretical (dashed grey line) and observed power spectra, [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Cross-correlation signals for the voids identified in the North ( [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Stacked images of the simulated cross-correlation from the Buzzard mocks ( [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Left: Cross-correlation signals for the voids identified in the full-sky DESI Legacy Survey and the corresponding calibrated Buzzard mock realizations. The measurements are provided for the full void samples and the three different λv bins considered. Right: Summarize…
Figure 13
Figure 13. Figure 13: Left: Tomographic cross-correlation signals for the voids identified in the full-sky DESI Legacy Survey and the corresponding calibrated Buzzard mock realizations. The measurements are provided for the full void samples and the three different λv bins, analyzed in fou…

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