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arxiv: 2512.07295 · v2 · submitted 2025-12-08 · 🌌 astro-ph.CO

Squeezed Limit non-Gaussianity Estimation with Cosmic Shear

Shi-Hui Zang , Moritz M\"unchmeyer This is my paper

Pith reviewed 2026-05-17 00:58 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial non-Gaussianitycosmic shearweak lensingsqueezed limitf_NLLSST surveypower spectrum modulation
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The pith

Cosmic shear data can reveal primordial non-Gaussianity through large-scale modulations of the local power spectrum.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a method to measure local primordial non-Gaussianity from cosmic shear observations by tracking how long-wavelength modes alter the small-scale lensing power spectrum. The technique builds on the π-field approach but adapts it for spherical geometry in weak lensing surveys. It requires only the binned large-scale power spectra C_ℓ and their covariance, avoiding the computational cost of a full bispectrum analysis while retaining the squeezed-limit signal. Validation on N-body simulations confirms accurate recovery of f_NL values. A Fisher forecast indicates that an LSST-like survey could achieve an uncertainty of roughly 44 on this parameter.

Core claim

The paper claims that the squeezed-limit primordial non-Gaussianity signal can be extracted from the modulation of the local lensing power spectrum using an extension of the π-field method to spherical coordinates. This estimator is simpler than a full bispectrum calculation yet captures the complete information, as demonstrated by successful validation on simulations and a projected constraint of σ_fNL ≃ 44 for LSST.

What carries the argument

The π-field method extended to spherical coordinates, which quantifies the response of the binned multipole power spectra to a large-scale modulating mode.

If this is right

  • The estimator needs only binned C_ℓ(z1,z2) on large scales and their covariance matrix.
  • Tests on N-body simulations show accurate recovery of input f_NL values.
  • A Fisher matrix forecast for an LSST-like weak lensing survey yields σ_fNL ≃ 44.
  • The method combines naturally with kSZ velocity reconstruction and clustering-based π-fields for joint analyses.

Where Pith is reading between the lines

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

  • This technique could be extended to other large-scale structure probes like galaxy clustering to enhance f_NL sensitivity.
  • Accounting for potential late-time contaminations would be necessary for real data applications to maintain signal purity.
  • Integration with CMB lensing or other observables might push the uncertainty below the forecasted value.

Load-bearing premise

The observed large-scale modulation in the local lensing power spectrum arises primarily from primordial squeezed non-Gaussianity without significant interference from late-time effects or unmodeled systematics.

What would settle it

Running the estimator on simulated lensing maps with known input f_NL values and checking if the output matches the input within expected errors would test the method's validity.

Figures

Figures reproduced from arXiv: 2512.07295 by Moritz M\"unchmeyer, Shi-Hui Zang.

Figure 1
Figure 1. Figure 1: Matter field model. Upper panel: The blue curves show the cross-power spectrum Cδmπ(ℓ) for matter fields and π fields from Ulagam simulations. The brown lines represent our best-fit models, with the dashed lines showing the contributions from the different terms in our model. The left, middle, and right panels correspond to cosmologies with input fNL = 0, fNL = 100, and fNL = −100, respectively. The redshi… view at source ↗
Figure 2
Figure 2. Figure 2: Range of validity of the model for matter. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Lensing field model in first of Ntomo = 3 case. Upper panel: The blue curves show the cross-power spectrum Cκgπ(ℓ) for lensing convergence fields and π fields from Ulagam simulations (using the first bin of three tomographic bins, with ℓ > 5). The brown lines represent our best-fit models, with the dashed lines showing the contributions from the different terms in our model. The left, middle, and right pan… view at source ↗
Figure 4
Figure 4. Figure 4: Redshift distribution for different tomographic bin numbers under LSST configuration. Here zmin and zmax is the lower bound and upper bound redshift of each tomographic bin. In this work, we investigate how the fNL constraint changes according to the number of tomographic bins with Ntomo = 1, 3, 5. For the three tomographic bin case, we divide the galaxies into three bins with equal number density. The red… view at source ↗
Figure 5
Figure 5. Figure 5: The forecasted constraints on fNL from cross power spectrum. The curves represent the cumulative information from ℓ hard min = 200 to ℓ hard max . The left panel shows the result with minimum soft mode cut-off ℓ soft min = 2, middle panel with ℓ soft min = 10 and right panel with ℓ soft min = 20. Black curves are result for one tomographic bin. Red curves represent results from three tomographic bins. Blue… view at source ↗
Figure 6
Figure 6. Figure 6: Fisher information for fNL with and without marginalizing over A0. One single tomographic bin of cos￾mic shear is assumed. The solid line represents the Fisher information given perfect knowledge of gravitation-induced non-Gaussianity, while the dashed line is the result marginal￾izes over A0. 1000 2000 3000 hard max 60 80 100 120 140 160 180 (fN L) soft min =2 =100 =500 [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
Figure 8
Figure 8. Figure 8: Gaussian bias (left) and non-Gaussian bias (right) for the π field for a matter shell. 10 1 10 2 10 3 10 2 C m z=0.99, W = [1000, 1010] Non-perturbative theory Linear Model 10 1 10 2 10 0 2 × 10 0 3 × 10 0 z=0.99, W = [1000, 1500] [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The comparison of two models (red for non-perturbative model and blue for linear model) at redshift z = 0.99. The solid lines are cosmology with fNL = 0, dashed lines for fNL = 100. The left panel is the results for narrow high-pass filter (ℓmin, ℓmax) = ([1000, 1010]). The right panel is for a wide high-pass filter (ℓmin, ℓmax) = ([1000, 1500]). The agreement is good for a wide high-pass filter, but break… view at source ↗
Figure 10
Figure 10. Figure 10: The comparison of two models (red for non-perturbative model and blue for linear model) for the matter field averaged between z = 0.99 to z = 1.5. The solid lines are cosmology with fNL = 0, dashed lines for fNL = 100. The left panel is the results for narrow high-pass filter (ℓmin, ℓmax) = ([1000, 1010]). The right panel is for a wide high-pass filter (ℓmin, ℓmax) = ([1000, 1500]). for a robust estimatio… view at source ↗
Figure 11
Figure 11. Figure 11: The comparison of two models (red for non-perturbative model and blue for linear model) for the third lensing convergence field with Ntomo = 3. The solid lines are cosmology with fNL = 0, dashed lines for fNL = 100. The left panel is the results for narrow high-pass filter (ℓmin, ℓmax) = ([1000, 1010]). The right panel is for a wide high-pass filter (ℓmin, ℓmax) = ([1000, 1500]). measurements from cosmic … view at source ↗
Figure 12
Figure 12. Figure 12: The matter power spectrum at multiple redshifts. The black lines are results averaged over 1000 simulations, red lines are calculated from CAMB with Eq. (16), blue bars are 1-σ uncertainties. The apparent oscillations are not due to cosmic variance but due to the simulation tiling. 20 40 60 0.0 0.5 1.0 1.5 2.0 C 1e 8 Tomo 1/3 CAMB Simulation 20 40 60 1 2 3 4 1e 8 Tomo 2/3 20 40 60 2 4 6 1e 8 Tomo 3/3 [PI… view at source ↗
Figure 13
Figure 13. Figure 13: The power spectrum of lensing fields. The black lines are results averaged over 100 simulations, red lines are calculated from CAMB with Eq. (16), blue bars are 1-σ uncertainties. In this work, generally the multipole ℓ of the cross-powers are much smaller than the multipoles filtered out by the high-pass filter, ℓ ≪ ℓHP. Under this assumption we can apply the following approximation (Varshalovich et al. … view at source ↗
Figure 14
Figure 14. Figure 14: The geometric factor N calculated in both analytical and approximated ways [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗
read the original abstract

We present a new method to constrain local primordial non-Gaussianity using the large-scale modulation of the local lensing power spectrum. Our work extends our recently proposed $\pi$-field method for primordial non-Gaussianity estimation to spherical coordinates and applies it to galaxy lensing. Our approach is computationally efficient and only requires binned multipole power spectra $C_\ell(z_1,z_2)$ on large scales, as well as their covariance. Our method is simpler to implement than a full bispectrum estimator, but still contains the full squeezed-limit information. We validate our model using a suite of N-body simulations and demonstrate its accuracy in recovering the $f_{\mathrm{NL}}$ values. We then perform a Fisher forecast for an LSST-like weak lensing survey, finding $\sigma_{f_{\mathrm{NL}}} \simeq 44$. Our approach readily combines with other $f_{\mathrm{NL}}$-sensitive fields such as kSZ velocity reconstruction and clustering-based $\pi$-fields, for a future combined $f_{\mathrm{NL}}$ estimator using various large-scale galaxy and CMB observables.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper extends the π-field formalism to spherical coordinates to estimate local primordial non-Gaussianity (f_NL) from the large-scale modulation of the cosmic shear power spectrum C_ℓ(z1,z2). It claims the approach is computationally simpler than a full bispectrum estimator while retaining the squeezed-limit information, validates the estimator on N-body simulations with accurate f_NL recovery, and reports a Fisher forecast of σ_fNL ≃ 44 for an LSST-like weak-lensing survey. The method is presented as readily combinable with kSZ and clustering-based probes.

Significance. If the assumption that late-time effects and higher-order terms do not contaminate the large-scale modulation holds, this provides an efficient route to f_NL constraints from upcoming lensing data that complements other large-scale observables. The N-body validation and Fisher forecast are concrete strengths, though their robustness depends on the handling of realistic systematics.

major comments (2)
  1. [N-body validation and model description] The central assumption that the binned large-scale C_ℓ(z1,z2) modulation isolates the primordial squeezed signal requires that projection effects, late-time gravitational couplings, intrinsic alignments, and terms beyond the leading spherical π-field extension remain negligible. The N-body validation recovers input f_NL but does not appear to include tests with these realistic contaminants at the relevant multipoles and redshifts, leaving the LSST forecast applicability uncertain.
  2. [Validation section] Covariance modeling details and quantitative recovery plots are not described in the abstract or validation summary; without explicit demonstration that the estimator remains unbiased under realistic survey masks, photo-z errors, and shape noise, the claimed accuracy in recovering f_NL values is only partially supported.
minor comments (2)
  1. Clarify the exact binning scheme for C_ℓ(z1,z2) and the multipole range used for the large-scale modulation to aid reproducibility.
  2. The abstract states the method 'contains the full squeezed-limit information'; a brief algebraic comparison to the standard squeezed bispectrum limit would strengthen this claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for providing constructive comments that help clarify the scope and limitations of our work. We address each major comment in turn below, with a focus on strengthening the presentation of our validation and assumptions.

read point-by-point responses

  1. Referee: [N-body validation and model description] The central assumption that the binned large-scale C_ℓ(z1,z2) modulation isolates the primordial squeezed signal requires that projection effects, late-time gravitational couplings, intrinsic alignments, and terms beyond the leading spherical π-field extension remain negligible. The N-body validation recovers input f_NL but does not appear to include tests with these realistic contaminants at the relevant multipoles and redshifts, leaving the LSST forecast applicability uncertain.

    Authors: We agree that the N-body validation is performed in a controlled setting without the full suite of observational contaminants. The simulations are used to verify that the estimator recovers the input f_NL when the only source of non-Gaussianity is the primordial squeezed signal, which directly tests the core extension of the π-field formalism to spherical coordinates. Late-time gravitational couplings and projection effects are suppressed in the squeezed limit on the large scales we consider, consistent with the theoretical derivation; intrinsic alignments are not included because the current implementation focuses on the lensing convergence field. We will revise the manuscript to add an explicit discussion subsection on the expected magnitude of these contaminants, their scale dependence, and why they remain subdominant for the LSST forecast. We will also outline how future work can incorporate them via more realistic mocks. revision: partial

  2. Referee: [Validation section] Covariance modeling details and quantitative recovery plots are not described in the abstract or validation summary; without explicit demonstration that the estimator remains unbiased under realistic survey masks, photo-z errors, and shape noise, the claimed accuracy in recovering f_NL values is only partially supported.

    Authors: The covariance is constructed from the suite of N-body realizations and is described in the methods and validation sections of the full manuscript, with quantitative recovery shown via direct comparison of estimated versus input f_NL. The abstract is necessarily concise and does not contain these details. To address the concern, we will expand the validation section to include (i) a clearer description of the covariance estimation procedure, (ii) additional quantitative plots with error bars and bias metrics, and (iii) a new paragraph discussing the impact of survey masks, photo-z errors, and shape noise. While the present validation assumes idealized conditions, the estimator operates on binned large-scale power spectra, which are relatively robust to small-scale noise; we will note this and indicate how these systematics can be forward-modeled in a full analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained with external validation

full rationale

The paper extends the authors' prior π-field framework to spherical coordinates for cosmic shear but introduces a new implementation whose outputs are not algebraically forced to match any input fit. Validation proceeds via independent N-body simulations that recover injected f_NL values, and the Fisher forecast follows standard methodology without self-referential closure. Self-citation to the earlier π-field work exists but is not load-bearing for the central claim, as the present analysis supplies new spherical binning, covariance handling, and simulation-based tests that stand apart from the cited prior. No step reduces by construction to a fitted parameter renamed as prediction or to an unverified uniqueness theorem imported from the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard cosmological assumptions about the origin of the squeezed bispectrum signal and the validity of the modulation picture; no new free parameters or invented entities are introduced beyond the target f_NL.

axioms (1)
  • domain assumption The squeezed-limit non-Gaussianity imprints a measurable large-scale modulation on the local small-scale lensing power spectrum.
    This is the foundational premise of the π-field method being extended here.

pith-pipeline@v0.9.0 · 5492 in / 1256 out tokens · 30434 ms · 2026-05-17T00:58:16.989263+00:00 · methodology

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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.

  1. If at First You Don't Succeed, Trispectrum: I. Estimating the Matter Power Spectrum Covariance with Higher-Order Statistics

    astro-ph.CO 2026-04 unverdicted novelty 6.0

    Estimators from squeezed bispectrum and collapsed trispectrum recover unbiased small-scale matter power spectrum covariance at the percent level using 25 Quijote simulations.

Reference graph

Works this paper leans on

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

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    work page doi:10.5281/zenodo.831784 2021