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Constraints on primordial non-Gaussianity from the cross-correlation of DESI Luminous Red Galaxies and $Planck$ CMB lensing

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Cross-correlating DESI luminous red galaxies with Planck CMB lensing keeps the local primordial non-Gaussianity parameter consistent with zero, and is more stable against imaging systematics than the galaxy autocorrelation.

desk verdict A careful, honest fNL constraint from the DESI LRG x Planck lensing cross-correlation that lands at zero within ~1 sigma; the robustness claim has a real gap around correlated lensing-systematics, but the paper deserves review. read the letter →

arxiv 2412.10279 v2 pith:5SMIQ3XA submitted 2024-12-13 astro-ph.CO

J. R. Bermejo-Climent , R. Demina , A. Krolewski , E. Chaussidon , M. Rezaie , S. Ahlen , S. Bailey , D. Bianchi
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D. Brooks E. Burtin T. Claybaugh A. de la Macorra Arjun Dey P. Doel G. Farren S. Ferraro J. E. Forero-Romero E. Gaztañaga S. Gontcho A Gontcho G. Gutierrez C. Hahn K. Honscheid C. Howlett R. Kehoe D. Kirkby T. Kisner M. Landriau L. Le Guillou M. E. Levi M. Manera A. Meisner R. Miquel J. Moustakas J. A. Newman G. Niz N. Palanque-Delabrouille W. J. Percival F. Prada I. Pérez-Ràfols D. Rabinowitz A. J. Ross G. Rossi E. Sanchez D. Schlegel D. Sprayberry G. Tarlé B. A. Weaver M. White C. Yèche P. Zarrouk
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classification astro-ph.CO
keywords primordialnon-Gaussianityf_NLscale-dependentgalaxybiasCMBlensingcross-correlationDESIluminousredgalaxiesimagingsystematicsangularpowerspectrum
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

The paper sets out to measure the local primordial non-Gaussianity parameter $f_{\rm NL}$ from the angular cross-correlation of about nine million DESI luminous red galaxies with Planck CMB lensing, exploiting the scale-dependent galaxy bias that a nonzero $f_{\rm NL}$ would imprint on the largest scales. Using the cross-correlation alone it finds $f_{\rm NL} = 39^{+40}_{-38}$ at 68% confidence, and combining with the LRG autocorrelation (with a scale cut to limit systematics) gives $f_{\rm NL} = 24^{+20}_{-21}$. Both results are consistent with zero primordial non-Gaussianity, meaning the data do not require non-Gaussian initial conditions. The paper's broader methodological claim is that the cross-correlation is less sensitive to imaging systematics than the autocorrelation, and that with proper neural-network mitigation this channel can help future surveys reach competitive $f_{\rm NL}$ constraints. A reader should care because a robust $f_{\rm NL}$ measurement is a direct test of the simplest inflationary models, which predict Gaussian initial conditions.

What carries the argument

The load-bearing mechanism is the scale-dependent galaxy bias induced by local primordial non-Gaussianity: parametrize the primordial potential as $\Phi = \phi + f_{\rm NL}(\phi^2 - \langle\phi^2\rangle)$; a nonzero $f_{\rm NL}$ adds a contribution $\Delta b(k,z) = 2(b_g - p) f_{\rm NL} \delta_{\rm crit} / \alpha(k)$ to the bias, which grows as $1/k^2$ and is therefore largest at the low multipoles where the cross-correlation is measured. The pipeline estimates $C_\ell^{\kappa G}$ and $C_\ell^{GG}$ from masked maps using pseudo-$C_\ell$ (NaMaster), models them with CAMB including lensing magnification and redshift-space distortions, and infers $f_{\rm NL}$ and the linear bias $b_0$ via an MCMC likelihood. A neural-network systematics mitigator (SYSnet) removes imaging contaminants from the LRG map before computing the spectra, and mock tests justify cutting the first multipole bin of $C_\ell^{GG}$ while keeping all multipoles of $C_\ell^{\kappa G}$.

What would settle it

Contaminate the mock CMB lensing maps with a template correlated with the LRG imaging systematics, for example dust extinction, and rerun the pipeline: if the recovered $f_{\rm NL}$ shifts by more than the 68% error bar, the claimed stability of $C_\ell^{\kappa G}$ fails. A simpler observational check is to cross-correlate the Planck lensing map with the dust template itself at the same multipoles; a significant signal would mean the cross-correlation is susceptible to the unmodeled correlation.

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Extended reading notes

Core claim

The central empirical claim is that the local primordial non-Gaussianity parameter is consistent with zero: $f_{\rm NL} = 39^{+40}_{-38}$ at 68% confidence from the LRG--CMB lensing cross-correlation $C_\ell^{\kappa G}$ alone, and $f_{\rm NL} = 24^{+20}_{-21}$ when combined with the LRG autocorrelation $C_\ell^{GG}$, with both within about one $\sigma$ of zero. The supporting methodological claim is that $C_\ell^{\kappa G}$ is more stable against imaging systematics than $C_\ell^{GG}$, because the cross-correlation is less affected by the excess large-scale power that contaminates the density maps; the paper demonstrates this stability by running the full pipeline on contaminated mocks and by showing that the $f_{\rm NL}$ constraint is robust to the choice of $\sigma_8$, bias evolution, and the PNG response parameter $p$. The analysis also reports a model-independent constraint on the product $b_\phi f_{\rm NL} = 146^{+154}_{-142}$, which remains compatible with Gaussian initial conditions.

Load-bearing premise

The analysis assumes there are no systematics correlated between the Planck CMB lensing map and the DESI LRG map; the mock validation adds contamination only to the LRG maps and leaves the lensing maps clean, so any real-world correlation between the two probes would bias the cross-correlation without being tested.

Editorial extensions

If this is right

  • Future $f_{\rm NL}$ measurements can exploit CMB lensing cross-correlations as a systematics-resistant observable, either alone or combined with galaxy autocorrelations.
  • Combining $C_\ell^{\kappa G}$ with $C_\ell^{GG}$ tightens the uncertainty from $\sigma(f_{\rm NL})\sim 40$ to $\sim 20$, even with a conservative scale cut on the autocorrelation.
  • The lowest multipole bin of the LRG autocorrelation ($\ell = 2$ to $6$) remains contaminated after mitigation, so scale cuts there are necessary for unbiased joint constraints.
  • The $f_{\rm NL}$ estimate is stable under changes in $\sigma_8$, the galaxy bias evolution, and the assumed response parameter $p$, supporting the robustness of the cross-correlation channel.

Reading between the lines

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

  • Because the mock validation contaminated only the LRG maps, the pipeline never tests for systematics correlated between Planck lensing and the LRG density; a mock test that adds the same foreground template to both maps would directly probe this blind spot.
  • The persistently positive best-fit values, such as $+39$ from $C_\ell^{\kappa G}$, could be a residual of the slight overfitting seen in mock tests, and might shift toward zero with a better-calibrated mitigation.
  • Since the observable is really the product $b_\phi f_{\rm NL}$, a simulation-calibrated $b_\phi$ beyond the universality assumption would convert the reported $b_\phi f_{\rm NL} = 146^{+154}_{-142}$ directly into a cleaner $f_{\rm NL}$ bound.
  • With future CMB lensing maps of lower noise and DESI's full spectroscopic sample, the same cross-correlation strategy could approach the forecast $\sigma(f_{\rm NL})\sim 5$, making it a competitive probe of inflaton dynamics.
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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 measures the local primordial non-Gaussianity parameter f_NL through the scale-dependent galaxy bias effect, using the angular cross-correlation between DESI DR9 luminous red galaxies (LRG) and Planck PR4 CMB lensing, and the LRG autocorrelation. The analysis pipeline consists of a SYSnet neural-network imaging systematics mitigation applied to the LRG maps, pseudo-C_ell estimation with NaMaster, a CAMB-based theoretical model including redshift-space distortions and lensing magnification with s=0.999, and MCMC inference over f_NL and a bias parameter (plus shot noise for the autocorrelation). The headline results are f_NL = 39+40/-38 (68% CL) from C_l^{kappa G} alone and f_NL = 24+20/-21 from the joint analysis with C_l^{GG}, with the autocorrelation using an ell_min=7 scale cut. The pipeline is tested on 100 correlated Gaussian mocks, including regressis-based imaging contamination.

Significance. If the constraints are unbiased, the paper provides an important demonstration that CMB lensing cross-correlations are a systematics-resistant avenue for f_NL measurements with photometric samples, with direct relevance to DESI and future surveys. The analysis is careful in many respects: end-to-end mock validation, multiple robustness tests (sigma8, p parameter, bias evolution, ell_min, NGC/SGC splits), and public release of data products are all strengths. However, the validation has a load-bearing gap: contamination is added only to the LRG mocks and not to the CMB lensing mocks, so correlated systematics between the two probes are explicitly assumed away. In addition, the scale cut for C_l^{GG} is motivated by mock tests but in the real data removes the bins showing the largest deviation, and the unblinded analysis leaves open the question of post-hoc selection. These issues do not invalidate the measurement, but they mean the 'robustness' claim currently outruns the evidence it is based on.

major comments (3)
  1. [§5, Fig. 7] The mock validation explicitly assumes no correlated systematics between the two probes: the text states 'we did not add any contamination to the CMB lensing mock fields. This was equivalent to assuming there is no correlation in systematics between the two probes.' This assumption is load-bearing for the central claim that C_l^{kappa G} is robust to imaging systematics. SYSnet acts only on the LRG overdensity map (§4.1), so a systematic that enters both the Planck lensing reconstruction and the LRG selection (e.g., Galactic dust or extinction patterns) would not be removed, and the tests presented here do not exercise that channel. The NGC/SGC split and the ell_min variations do not close the gap because they do not change the shared foreground physics. I would ask for a specific null test, for example cross-correlating the mitigated LRG map with Planck lensing systematics maps or with lensing maps reconstructed from different frequency estimators; at minimum, the paper should state and quantify the residual foreground contamination that is assumed to be negligible for this measurement.
  2. [§4.2 and Fig. 12] The ell_min=7 cut for C_l^{GG} was chosen after inspecting mock tests, but in the real data it removes the lowest-multipole bins that show the largest discrepancy from f_NL=0: the text reports approximately a 2-sigma deviation for ell_min=2 and a 1-sigma deviation for ell_min=7. Because the measurement is explicitly unblinded, it should be documented at which stage this scale cut was frozen, and the full results for ell_min=2 (including the C_l^{GG}-only and joint fits) should be reported as primary or secondary numbers. Without this, the reader cannot distinguish a pre-specified robustness cut from a posteriori tuning to reduce the impact of a statistical fluctuation.
  3. [§5, Tables 1 and 2] The mock validation shows systematic biases that are not negligible compared to the statistical uncertainties. For example, for the f_NL=50 contaminated and mitigated mocks, C_l^{kappa G} alone returns 21 +/- 32, which is approximately 0.9 sigma below the input; for the f_NL=-50 mocks, the joint constraint returns -30 +/- 27, about 1 sigma above the input. The statement that the input f_NL is always within 1 sigma is formally correct but weak for the paper's robustness claim, because a bias comparable to the quoted 1-sigma error is exactly what the measurement is trying to exclude. The paper should either add a systematic-error term to the covariance or the likelihood, apply a calibration based on the mocks, or explicitly soften the conclusion from 'robust' to 'consistent within the current statistical precision.'
minor comments (4)
  1. [Introduction] There are typographical errors: 'louminous red galaxy' and 'line of slight' should be corrected.
  2. [Fig. 2 caption] The caption reads 'after applying the δ < -30º cut'; this should be 'declination < -30 degrees' for clarity.
  3. [§3.2] The statement that the multiplicative Monte Carlo correction is generally less than about 5% but reaches 10-12% on the largest scales is important for the low-ell f_NL signal; it would help to show the correction as a small figure or table, although the current text is acceptable.
  4. [§4.2] The covariance is computed with the analytic Gaussian covariance function using a smoothed version of the measured power spectra as input, and the paper says a mock-based covariance gives compatible results. It would be useful to state whether the smoothed input includes the residual systematics power or the mitigated power, since this choice can affect the error bars by tens of percent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the f_NL measurement is an external-model fit to data, not a renaming of its inputs.

full rationale

The central claim f_NL = 39+40/-38 is obtained by fitting CAMB-computed angular power spectra to the measured C_l^{kappa G} and C_l^{GG}, with the local-PNG scale-dependent bias of Eq. (2) as the physical model. The non-Gaussian parameter is not defined in terms of the measured spectra, nor is any fitted parameter renamed as a prediction. The key inputs are external or independently measured: dN/dz from DESI Survey Validation spectra, s = 0.999 from Kitanidis & White (2021), sigma8 = 0.77 from ACT-lensing cross-correlations, and the CAMB code. The adoption of the SYSnet 'nonlinear three maps' mitigation recipe from Rezaie et al. (2024) is a methodological inheritance from a partly overlapping collaboration, but it is not load-bearing in a circular sense: the pipeline is re-validated on contaminated mocks in Section 5, and the recipe is one of several tested choices. The covariance matrix is computed using smoothed measured power spectra as input; this makes the error bars partly data-dependent but does not enter the model prediction for the signal and cannot force the recovered f_NL. The paper itself flags the limitation that mock validation adds contamination only to LRG maps, 'equivalent to assuming there is no correlation in systematics between the two probes.' That is an untested systematics assumption and a legitimate robustness concern, but it is not a circularity: no equation of the analysis reduces to itself, and no external benchmark is replaced by a self-citation. The comparison against external measurements (Planck bispectrum, eBOSS/DESI LSS constraints) further confirms the result is a genuinely new fit rather than a restatement of inputs.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central measurement is an empirical fit. The model uses external inputs (dN/dz from DESI SV spectra, magnification bias s = 0.999 from Kitanidis & White 2021, sigma8 = 0.77 from ACT x LRG) and modeling assumptions (universality relation with p = 1, bias evolution b0 D(z)^{-1}, no correlated systematics between the two maps). The fitted parameters are f_NL, b0, and shot noise. No new physical entities are introduced.

free parameters (3)
  • f_NL = 39 +40/-38 (cross-correlation); 24 +20/-21 (combined)
    Target parameter of the measurement, constrained by the likelihood via the scale-dependent galaxy bias.
  • b0 (galaxy bias at z=0) = 1.51 ± 0.05 (cross-correlation); 1.48 ± 0.02 (combined)
    Linear bias amplitude fitted jointly with f_NL; controls the amplitude of CGG and CkappaG.
  • Nshot (shot noise for CGG)
    Nuisance parameter for the autocorrelation; absorbs unknown stochastic contribution. Central value not reported in the paper.
assumptions (6)
  • domain assumption The universality relation for the scale-dependent bias (Slosar et al. 2008), Eq. (2), with p = 1 (baseline) or p = 0.55 (robustness), holds for LRGs.
    This relation converts the measured scale-dependent bias into a constraint on f_NL. If the true response p differs, the inferred f_NL shifts: the paper finds f_NL = 29 +25/-27 for p = 0.55 instead of 39 +40/-38 for p = 1. The qualitative conclusion of consistency with zero is unchanged.
  • domain assumption The galaxy bias evolves as b(z) = b0 * D(z)^{-1} (Zhou et al. 2021).
    Assumed redshift evolution for the LRG sample. The paper tests a free exponent and finds full consistency, so this is a mild assumption.
  • domain assumption The magnification bias is fixed to s = 0.999 and is redshift-independent (Kitanidis & White 2021).
    Lensing magnification contributes up to about 35% of the predicted CkappaG at low multipoles (Figure 4). An incorrect s would bias the model amplitude and therefore the fitted f_NL.
  • domain assumption There are no systematics correlated between the Planck CMB lensing map and the DESI LRG map.
    The mock validation contaminates only the LRG maps: 'we did not add any contamination to the CMB lensing mock fields. This was equivalent to assuming there is no correlation in systematics between the two probes' (Section 5). If galactic foregrounds affect both probes, the cross-correlation would be biased in a way this pipeline cannot test.
  • domain assumption The analytic Gaussian covariance computed by NaMaster, using smoothed measured power spectra as input, is an adequate description of the errors.
    The covariance is not estimated from the simulations in the baseline analysis; using data-derived spectra as input could make the error bars slightly data-dependent. The authors report agreement with a mock-based covariance as a cross-check.
  • ad hoc to paper Mock contamination generated with regressis and SYSnet weights reproduces the real imaging systematics.
    The validation's fidelity depends on this contamination model; the real systematics could be more complex, which would change the inferred scale cuts and bias corrections.

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Cite this review

Pith. "Pith review of Constraints on primordial non-Gaussianity from the cross-correlation of DESI Luminous Red Galaxies and $Planck$ CMB lensing." pith.science (2026). https://pith.science/paper/5SMIQ3XA

@misc{pith2026241210279,
  author       = {Pith},
  title        = {Pith review of: Constraints on primordial non-Gaussianity from the cross-correlation of DESI Luminous Red Galaxies and $Planck$ CMB lensing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5SMIQ3XA}},
  note         = {Machine review of arXiv:2412.10279}
}
abstract

We use the angular cross-correlation between a luminous red galaxy (LRG) sample from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey data release DR9 and the $Planck$ cosmic microwave background (CMB) lensing maps to constrain the local primordial non-Gaussianity parameter, $f_{\rm NL}$, using the scale-dependent galaxy bias effect. The galaxy sample covers approximately 40\% of the sky, contains galaxies up to redshift $z \sim 1.4$, and is calibrated with the LRG spectra that have been observed for DESI Year 1 (Y1). We apply a nonlinear imaging systematics treatment based on neural networks to remove observational effects that could potentially bias the $f_{\rm NL}$ measurement. Our measurement is performed without blinding, but the full analysis pipeline is tested with simulations including systematics. Using the two-point angular cross-correlation between LRG and CMB lensing only ($C_\ell^{\kappa G}$) we find $f_{\rm NL} = 39_{-38}^{+40}$ at 68% confidence level, and our result is robust in terms of systematics and cosmology assumptions. If we combine this information with the autocorrelation of LRG ($C_\ell^{GG}$) applying a $\ell_{\rm min}$ scale cut to limit the impact of systematics, we find $f_{\rm NL} = 24_{-21}^{+20}$ at 68% confidence level. Our results motivate the use of CMB lensing cross-correlations for measuring $f_{\rm NL}$ with future datasets given its stability in terms of observational systematics compared to the angular auto-correlation. Furthermore, performing accurate systematics mitigation is crucially important in order to achieve competitive constraints on $f_{\rm NL}$ from CMB lensing cross-correlation in combination with the tracers' autocorrelation.

Figures

Figures reproduced from arXiv: 2412.10279 by the authors.

Figure 1
Figure 1. Normalized redshift distribution of the LRG sample, directly measured using the spectroscopic redshifts from DESI Y1 data. 3. Datasets We describe in this section the datasets involved in our analy￾sis. The two main ingredients were an LRG photometric cata￾log from the DR9 Legacy Survey (Zhou et al. 2023b) and the Planck PR4 public CMB lensing maps (Carron et al. 2022). We also used an LRG spectroscopic sample from … view at source ↗
Figure 2
Figure 2. Left panel: LRG overdensity field in galactic coordinates, after applying the δ < -30º cut. Right panel: CMB lensing field in galactic coordinates, obtained from the Planck PR4 maps. 10 1 10 2 10 7 10 6 10 5 10 4 C C GG (raw) C GG (mitigated) C G (raw) C G (mitigated) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Angular power spectra of the LRG autocorrelation, C GG ℓ , and CMB lensing - LRG cross-correlation, C κG ℓ , obtained from the raw (un￾corrected) data and after applying the systematics mitigation pipeline to the LRG maps. plates. This pipeline is implemented in the SYSnet code, which is publicly available3 . In Rezaie et al. (2024), a detailed study of the performance of SYSnet was done using this LRG sample, with … view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Correlation matrix as obtained from the joint covariance matrix for C GG ℓ and C κG ℓ computed with the NaMaster code. available NaMaster code by Alonso et al. (2019). The pseudo￾Cℓ of a pair of fields can be defined as C˜XY ℓ = 1 2ℓ + 1 X m XℓmY ∗ ℓm , (18) where X an…
Figure 6
Figure 6. Figure 6: Single Gaussian realization of an LRG map before adding contamination (left panel) and after applying regressis to contaminate the mock (right panel). fNL and the galaxy bias at z = 0, b0, as the two main cosmolog￾ical parameters of interest to constrain. We assumed a …
Figure 7
Figure 7. Figure 7: Mean angular power spectra of the full sample LRG autocorrelation (left panels) and LRG-CMB lensing cross-correlation (right panels), computed from the 100 mock realizations used to test our pipeline for various values of fNL (-50 top panels, 0 middle panels, and 50 bo…
Figure 8
Figure 8. Figure 8: 1σ and 2σ confidence ellipses for the joint posterior distribution of the fNL and b0 parameters obtained from the C κG ℓ cross-correlation (grey contours), the C GG ℓ autocorrelation (red contours), and both ob￾servables jointly (blue contours). 100 0 100 200 fNL 1.2 1…
Figure 9
Figure 9. Figure 9: 1σ and 2σ confidence ellipses for the joint posterior distribution of the fNL and b0 parameters obtained from the C κG ℓ cross-correlation. The green contours assume the baseline σ8 value preferred by the LRG sample used in this paper, while the grey, red, and blue con…
Figure 10
Figure 10. Figure 10: 1σ and 2σ confidence ellipses for the joint posterior dis￾tribution of the fNL and b0 parameters obtained from the C κG ℓ cross￾correlation. The red contours correspond to the baseline constraints as￾suming p = 1, while the blue contours assume p = 0.55, as suggested …
Figure 11
Figure 11. Figure 11: 1σ and 2σ confidence ellipses for the joint posterior dis￾tribution of the fNL and b0 parameters obtained from the C κG ℓ cross￾correlation. The blue contours correspond to the baseline constraints after applying the SYSnet mitigation weights to the data and the red c…

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Forward citations

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