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REVIEW 3 major objections 4 minor 5 cited by

Tomographic analyses of the CMB lensing and galaxy clustering to probe the linear structure growth

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The linear growth of structure between redshifts 0.1 and 0.7 is consistent with the ΛCDM prediction, at measured amplitude $A_D = 1.16 \pm 0.13$.

desk verdict A careful, competent tomographic D_G measurement on a new photometric catalogue; the headline A_D = 1.16 ± 0.13 is plausible but rests on a single-Gaussian photo-z error model that the paper itself shows is shaky at z > 0.5. read the letter →

arxiv 1908.04854 v2 pith:OVII2GFB submitted 2019-08-13 astro-ph.CO

Gabriela A. Marques , Armando Bernui This is my paper · ORCID
classification astro-ph.CO
keywords cosmicmicrowavebackgroundlensinggalaxyclusteringtomographiccross-correlationlinearstructuregrowthbiasphotometricredshiftsLambdaCDMangularpowerspectrum
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 combines the auto-correlation of a 20-million-galaxy photometric sample with its cross-correlation against CMB lensing, in six redshift slices from $0.1

What carries the argument

The load-bearing object is the $\hat{D}_G$ estimator, a weighted ratio $$\hat{D}_G = \left\langle \frac{(C_\$ell^{{\kappa g}}$)_{\rm obs}/(C_\$ell^{{\kappa g}}$)_{\rm th}}{\sqrt{(C_\$ell^{{gg}}$)_{\rm th}/(C_\$ell^{{gg}}$)_{\rm obs}}} \right\rangle_\ell,$$ where the theoretical spectra are evaluated at $z=0$ with the growth factor removed. Because the galaxy auto-spectrum scales as $b^2 D^2$ and the cross-spectrum as $b D^2$, the combination cancels the linear galaxy bias $b$ and isolates the growth factor $D(z)$, normalized to $D(0)=1$. The machinery also includes the Limber-approximated power spectra, the linear and scale-independent bias model, jackknife and Monte-Carlo covariance estimates, and a conservative multipole cut where nonlinear corrections stay below 5%.

What would settle it

Take a large spectroscopic subsample of the same galaxy catalogue in the $0.5<z<0.7$ bins, use the empirical photo-z error distribution in place of the assumed Gaussian with $\sigma_z=0.019$, rebuild $dn/dz$, and refit $A_D$; a shift larger than about $1\sigma$ away from $A_D=1.16$ would falsify the claimed consistency.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is a tomographic measurement of the linear growth factor $D(z)$ that does not depend on knowing the galaxy bias. Using the auto-power spectrum of galaxy density and the cross-power spectrum with the Planck CMB lensing convergence, the authors derive $\hat{D}_G$ in six bins and fit its overall amplitude against the fiducial $\Lambda$CDM template, obtaining $A_D=1.16\pm0.13$, in agreement with $A_D^{\Lambda CDM}=1$. The galaxy bias fitted in each bin agrees with the cross-correlation amplitude within $1\sigma$, indicating a lensing amplitude consistent with unity; a lower amplitude seen in the full non-tomographic sample is traced to the high-redshift bins, where the photometric redshift uncertainties are largest. Null tests and foreground checks show no significant contamination of the cross-correlation.

Load-bearing premise

The result rests on the assumption that the reconstructed redshift distribution in each bin is correct, with photometric redshift error $\sigma_z=0.019$; if photo-z's are systematically underestimated at $z\gtrsim0.6$, the theoretical spectra shift and the fitted growth amplitude changes.

Editorial extensions

If this is right

  • If $A_D=1.16\pm0.13$ is correct, no significant deviation from $\Lambda$CDM growth exists in $0.1<z<0.7$; modified-gravity or dark-energy models that change $D(z)$ in this interval are constrained.
  • The bias-independent $\hat{D}_G$ method yields usable growth points from photometric surveys alone, which otherwise cannot measure $f\sigma_8$.
  • The per-bin agreement between galaxy bias and lensing amplitude supports treating the galaxy bias as linear and deterministic on the scales used.
  • The high-redshift-driven $A<b$ tension implies that tomographic treatment is preferable to a single-bin analysis when photometric redshift quality varies with redshift.

Reading between the lines

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

  • A direct spectroscopic calibration of the photo-z errors in the $0.5<z<0.7$ bins is the natural extension; given the paper's own finding that inferred bias shifts by up to 30% when $\sigma_z$ is changed, such a calibration could move $A_D$ toward or away from 1.
  • Applying the same estimator to lensing maps from upcoming CMB experiments combined with wide photometric surveys should reduce the statistical error on $A_D$ well below 10%, turning the consistency test into a sharp growth-index measurement.
  • The estimator could also be cross-correlated with galaxy shear instead of density, providing an independent bias-free growth measurement that shares no photo-z-dependent selection with the galaxy density map.
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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

3 major / 4 minor

Summary. The paper presents a tomographic measurement of the linear growth of structure using the cross-correlation between Planck CMB lensing and a galaxy overdensity map built from the SCUSS/SDSS/WISE photometric catalogue. The analysis splits the sample into six redshift bins over 0.1 < z < 0.7, measures galaxy auto and galaxy-CMB lensing cross power spectra with a pseudo-C_l (MASTER) estimator, and fits galaxy bias and the lensing amplitude in each bin. It then applies the bias-independent D_G estimator of Giannantonio et al. (2016) to constrain the linear growth factor, obtaining A_D = 1.16 ± 0.13 relative to the fiducial Planck cosmology, consistent with ΛCDM. The paper includes extensive systematics tests: tSZ deprojection, extinction masking, null tests with simulated maps, and a comparison of jackknife, Monte Carlo, and analytic covariances.

Significance. If the result holds, this is a useful new measurement of the growth of linear density fluctuations at z < 0.7 from a photometric survey covering a different sky region than previous analyses, and it is consistent with Planck ΛCDM. The paper's strengths are its careful pseudo-C_l implementation, the explicit validation of the covariance matrix against analytic and Monte Carlo estimates, and the battery of null and foreground tests. The main weakness is the reliance on a single-Gaussian photo-z error model and the poor goodness-of-fit in the two highest redshift bins, which may bias the headline A_D in a way not captured by the quoted statistical error.

major comments (3)
  1. [§5.3, Eq. (5.2)] The headline amplitude A_D = 1.16 ± 0.13 is obtained from a fit to all six redshift bins, including the two highest-z bins whose galaxy auto-spectra are poorly fitted (Table 2: PTE = 0.59% and 0.006%). Section 5.1 shows that the galaxy bias in those bins shifts by up to ~30% when σz is changed to 0.04 or 0.0, but the analysis never propagates these variations to D̂G or A_D. Because D̂G in Eq. (2.7) is not dn/dz-independent—the slashed theoretical spectra are computed from the assumed dn/dz—an incorrect or non-Gaussian photo-z error can bias A_D by an amount not reflected in the quoted 0.13 error. The authors should recompute D̂G and A_D with an empirical photo-z error distribution, or at least with the σz = 0.04 and σz = 0.0 variants already used in §5.1, and report the resulting shift in A_D. They should also quantify how much the two high-z bins pull the combined A_D, for example by comparing the six-bin fit to a fit that excludes those bins with a proper account of the covariance.
  2. [Abstract and §5.2] Table 2 reports PTE = 0.006% for the galaxy-galaxy fit in the 0.6 < z < 0.7 bin, yet the Abstract and Conclusions state that no significant evidence for systematic effects is found. Even if the poor fit is attributed to the known photo-z underestimation at z ≳ 0.6 (as argued in §5.1), a 0.006% PTE is itself a detected model-data discrepancy in a bin that enters the headline A_D fit. The language of the paper should be qualified, and the A_D result should be presented with the caveat that two of the six bins are not well described by the assumed dn/dz model.
  3. [§4.2 and §5.3] The D̂G error bars and the A_D uncertainty are computed from 500 Gaussian Monte Carlo realizations that are generated using the same assumed dn/dz and the fiducial cosmology (Section 4.3). These errors therefore account only for statistical fluctuations given the model, not for the uncertainty in the redshift distribution. Since §5.1 demonstrates that the inferred bias depends strongly on σz in the high-z bins, the D̂G errors are likely understated; at minimum, the photo-z contribution to the A_D error should be estimated by repeating the D̂G pipeline for the σz = 0.04 and σz = 0.0 cases or with a more realistic photo-z error model derived from the spectroscopic training sample.
minor comments (4)
  1. [Title and Abstract] The word "Tomographic" appears as "T omographic" in the title and abstract; in addition, the sentence in §5.3 beginning "Wecanassesstheamplitudeofthelineargrowthfunction..." is missing spaces between words.
  2. [§4.1] The phrase "we set the lowest value of ell on ell_min = 20" should read "we set the lowest value of ell to ell_min = 20".
  3. [Table 1] The galaxy counts in Table 1 (e.g., "2,208869", "3,178981") lack commas in the thousands separators, which makes the numbers difficult to read.
  4. [§4.3 and Appendix A] The comparison between jackknife and Monte Carlo covariances is valuable, but the sentence explaining that the JK off-diagonal terms "may incorporate also the non-Gaussian variance produced on small scales by the nonlinear evolution" is awkward; please rephrase for clarity. Additionally, the D̂G weighting in Eq. (4.8) appears to use the analytic errors of Eq. (4.6) while the parameter fits in §5.1 use the JK covariance; the paper should state explicitly which errors are used in the D̂G weighting and justify that choice.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the A_D measurement is a null-test ratio against the fiducial Planck cosmology, with the data entering directly and able to disagree.

full rationale

The central claim, A_D = 1.16 ± 0.13, is obtained from the bias-independent estimator Dhat_G defined in Eq. (2.7), which forms ratios between observed Cgg and Ckappa-g bandpowers and theoretical spectra computed from the fiducial Planck 2018 cosmology. This is a null-test normalization, not a self-definitional reduction: the observed spectra enter the ratio directly, so if the growth amplitude or shape differed from the fiducial model, Dhat_G would move away from D_fid. No fitted parameter is renamed as a prediction; the galaxy bias b and cross-correlation amplitude A are fitted in §5.1, but Dhat_G is computed bin by bin via Eqs. (4.7)-(4.9), and the amplitude A_D is then obtained by a separate fit to the D_fid template in Eq. (5.2). The paper even reports the high-redshift bins having poor PTE, demonstrating that the data can and do disagree with the fiducial template at some level. The photo-z error input, sigma_z = 0.019 from the external catalogue paper [47], is a data-calibration assumption, and the paper explicitly tests its impact by varying sigma_z; any inadequacy there is a systematic/correctness concern, not circularity. The self-citations in the introduction (e.g., [8], [9]) are contextual and not load-bearing. No equation reduces to its own input and no external result is imported to force the conclusion, so the derivation is self-contained and non-circular.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

All parameters in the central chain are fitted to data rather than derived from first principles: b and A per bin, and A_D as the headline result. The photo-z distribution and linear bias model are input assumptions imported from external catalogues and standard theory. No new entities are postulated.

free parameters (3)
  • Galaxy bias b in each redshift bin = 0.79, 0.79, 0.84, 0.86, 0.85, 0.81 (Table 2)
    Fitted to the galaxy auto-power spectrum per bin; needed for bias constraints and A comparisons, though D_G is designed to be independent of b.
  • Cross-correlation amplitude A = b A_lens per bin = 1.01, 0.92, 0.80, 0.76, 0.76, 0.81 (Table 2)
    Fitted to galaxy-CMB lensing cross-spectra; used to test lensing amplitude consistency.
  • Growth amplitude A_D = 1.16 ± 0.13 (main); 1.22 ± 0.19 using three lowest bins
    Fitted by D_G(z) = A_D D_fid(z) in eq. 5.2; this is the central result.
assumptions (5)
  • domain assumption Planck 2018 ΛCDM fiducial cosmology
    Used to compute theoretical C_l via CAMB/Halofit and D_fid(z); the measured growth amplitude is relative to this model (§2, §5.3).
  • domain assumption Linear, deterministic, scale-independent galaxy bias b(z)
    Eqs. 2.4 and 2.6 require this to write Cgg ∝ b^2 D^2 and Cκg ∝ b D^2, and for D_G bias cancellation.
  • domain assumption Gaussian photo-z error p(z|zph) with σz = 0.019 from [47]
    Eq. 3.2 reconstructs dn/dz; the paper's own robustness test shows bias changes up to 30% for σz = 0.0 or 0.04, so this is load-bearing.
  • domain assumption Limber approximation accurate at l > 10
    Used to convert 3D power spectra to angular power spectra in eq. 2.5; the paper restricts to l > 20.
  • domain assumption Halofit non-linear model and 5% linear/non-linear deviation cut define lmax
    Theoretical spectra use CAMB with Halofit; the scale cut assumes this model is reliable at the used scales.

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Cite this review

Pith. "Pith review of Tomographic analyses of the CMB lensing and galaxy clustering to probe the linear structure growth." pith.science (2026). https://pith.science/paper/OVII2GFB

@misc{pith2026190804854,
  author       = {Pith},
  title        = {Pith review of: Tomographic analyses of the CMB lensing and galaxy clustering to probe the linear structure growth},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OVII2GFB}},
  note         = {Machine review of arXiv:1908.04854}
}
abstract

In a tomographic approach, we measure the cross-correlation between the CMB lensing reconstructed from the Planck satellite and the galaxies of the photometric redshift catalogue based on the combination of the South Galactic Cap u-band Sky Survey (SCUSS), Sloan Digital Sky Survey (SDSS), and Wide-field Infrared Survey Explorer (WISE) data. We perform the analyses considering six redshift bins spanning the range of $0.1 <z<0.7$. From the estimates of the galaxy-galaxy and galaxy-CMB lensing power spectrum, we derive the galaxy bias and the amplitude of the cross-correlation for each redshift bin. We have finally applied these tomographic measurements to estimate the linear structure growth using the bias-independent $\hat{D}_{G}$ estimator introduced by Giannantonio et al. 2016. We find that the amplitude of the structure growth with respect to the fiducial cosmology is $A_{D}=1.16\pm 0.13$, closely consistent with the predictions of the $\Lambda$CDM model ($A_{D}^{\Lambda CDM}=1$). We perform several tests for consistency of our results, finding no significant evidence for systematic effects.

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Forward citations

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Reference graph

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