Weak Lensing Low Multipoles

Albert Bonnefous; Roya Mohayaee

arxiv: 2602.04504 · v3 · submitted 2026-02-04 · 🌌 astro-ph.CO

Weak Lensing Low Multipoles

Albert Bonnefous , Roya Mohayaee This is my paper

Pith reviewed 2026-05-16 07:21 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords weak lensingconvergence multipolescosmic dipole anomalylocal structure2MRSlarge-scale structureN-body simulations

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The pith

Weak lensing by local structure contributes at most a few percent to the cosmic dipole anomaly.

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

The paper examines the low-multipole components of the weak-lensing convergence field, which capture the largest-angle coherent potential gradients across the sky. Analytical expressions for the convergence power spectrum show that the dipole, quadrupole and octupole saturate at amplitudes around 10^{-4} in standard cosmology once sources lie at moderate redshifts. Full-sky N-body simulations demonstrate that observers in Milky Way-like environments record larger low-multipole signals than random observers. A reconstruction of the local convergence field from the 2MRS catalogue, after incompleteness and bias corrections, produces low multipoles above the mean prediction yet fully consistent with the Milky Way-like simulation subset. Converting the convergence dipole into an equivalent number-count dipole shows that weak lensing from nearby structure accounts for only a few percent of the observed anomaly in high-redshift catalogues.

Core claim

In a standard FLRW universe the dipole, quadrupole and octupole of the weak-lensing convergence saturate at amplitudes of order 10^{-4} once source redshifts exceed a few tenths. Full-sky N-body simulations demonstrate that observers placed in Milky Way-like environments measure larger low-multipole signals than random observers. A reconstruction of the local convergence field from the 2MRS catalogue, after corrections for incompleteness and bias, yields low multipoles that exceed the mean ΛCDM prediction yet remain consistent with the Milky Way-like subset of the simulations. Transforming the convergence dipole into an equivalent number-count dipole shows that weak lensing from local matter

What carries the argument

The local convergence field reconstructed from the 2MASS Redshift Survey, whose low-multipole moments are computed and then converted into an equivalent number-count dipole.

If this is right

The low multipoles reach their full amplitude by moderate source redshifts.
Milky Way-like observers record systematically larger low-multipole signals than average observers.
The 2MRS-reconstructed low multipoles match the distribution expected for observers in environments like ours.
Weak lensing from local structure contributes at most a few percent to the number-count dipole anomaly.

Where Pith is reading between the lines

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

Explanations for the dipole anomaly must therefore lie outside standard local lensing, such as survey selection effects or departures from the assumed cosmology.
The same reconstruction technique could be applied to other large-scale anomalies that align with the CMB dipole direction.
Deeper surveys will allow direct comparison of lensing convergence at higher redshifts to test whether the local signal grows as predicted.

Load-bearing premise

The 2MRS reconstruction with its incompleteness and bias corrections accurately recovers the true local convergence field that would be measured by a distant observer.

What would settle it

A direct measurement of the convergence dipole from a deeper, volume-complete galaxy survey at higher redshift that yields a value several times larger or smaller than the 2MRS-based prediction.

read the original abstract

We analyse the low--multipole components of the weak-lensing convergence field in a FLRW universe. The low--multipole convergence field, encodes the largest-angle coherent potential gradients, essential for assessment of large-angle features in data. To study this large angle signal, we perform a combined analytical, numerical and observational study. Starting from exact analytical expressions for the convergence power spectrum, we quantify how the dipole, quadrupole and octupole build up with source redshift and show that, in $\Lambda$CDM, they saturate at an amplitude of order $10^{-4}$. We then use full-sky, horizon-scale $N$-body simulations (Quijote) to explore the dependence of this signal on the observer's environment, comparing random observers to ``Milky Way--like'' observers. In parallel, we reconstruct the convergence field due to our local Universe with the 2MASS Redshift Survey (2MRS), with proper treatment of incompleteness and galaxy bias. We find that the observed low multipoles from observation is above the $\Lambda$CDM mean predictions, but in full agreement with Milky Way--like observers in the simulation. Finally, by converting the convergence dipole into a number-count dipole, we test whether weak lensing can contribute to the cosmic dipole anomaly, an idea motivated by its natural alignment with the CMB dipole and by the fact that lensing, unlike clustering, cannot be removed by cross-matching surveys and thus survives in all high-redshift catalogues. We show that weak lensing by local structure contributes at most a few percent to this observed anomaly.

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.

Desk Editor's Note private letter to a colleague

The paper puts a concrete few-percent upper limit on local lensing's contribution to the galaxy dipole anomaly by combining analytic saturation values, Quijote observer splits, and a 2MRS reconstruction.

read the letter

The central result is that weak lensing by local structure adds at most a few percent to the observed cosmic dipole anomaly. They reach this by converting the reconstructed convergence dipole into a number-count dipole and comparing it directly to the anomaly amplitude. The analytic part shows the dipole, quadrupole, and octupole in the convergence field saturate around 10^{-4} in Lambda-CDM once sources are far enough. The Quijote runs then check how much this signal varies for Milky-Way-like observers versus random ones, and the 2MRS map supplies the actual local field after incompleteness and bias corrections. The observed low multipoles sit above the mean Lambda-CDM prediction but line up with the MW-like observers in the simulations. That cross-check is the most useful piece here. It moves the discussion from qualitative arguments to a quantified bound that survives in high-redshift catalogs where clustering can be removed. The reconstruction step is the load-bearing part. The abstract claims proper treatment of incompleteness and bias, but the bound would loosen if those corrections systematically suppress large-scale power or misestimate the effective bias on the dipole. The Quijote comparison tests environment dependence, not the fidelity of the 2MRS pipeline itself on real data. A short validation test recovering a known input dipole through the same corrections would have strengthened the claim. This work is aimed at people tracking the dipole tension between CMB and galaxy surveys. It supplies a clean negative result that narrows the list of viable explanations without claiming to solve the anomaly. The methods are straightforward enough that a referee could check the error propagation and mask handling in one pass. I would send it to review.

Referee Report

3 major / 2 minor

Summary. The manuscript analyzes low-multipole (dipole, quadrupole, octupole) components of the weak-lensing convergence field in flat ΛCDM. Starting from exact analytical expressions for the convergence power spectrum, it shows these multipoles saturate at ~10^{-4} amplitude with source redshift. Full-sky Quijote N-body simulations compare random versus Milky Way-like observers. The local convergence field is reconstructed from the 2MRS survey with incompleteness and galaxy-bias corrections; the observed low multipoles exceed the ΛCDM mean but match MW-like observers. Converting the convergence dipole to a number-count dipole yields the central claim that local weak lensing contributes at most a few percent to the cosmic dipole anomaly.

Significance. If the few-percent upper bound is robust, the result meaningfully constrains one proposed explanation for the cosmic dipole anomaly, a persistent large-scale tension. The combination of analytic saturation results, horizon-scale simulations, and direct 2MRS reconstruction is a methodological strength; the explicit comparison to MW-like observers adds environmental context that is often missing from anomaly studies.

major comments (3)

[Abstract and §4] Abstract and §4 (2MRS reconstruction): the central claim that local lensing contributes 'at most a few percent' rests on the accuracy of the incompleteness and bias-corrected 2MRS convergence dipole. No quantitative recovery metric (e.g., fraction of injected dipole recovered in controlled mocks with known input density field) is reported, so it is unclear whether the pipeline systematically suppresses large-scale power or underestimates the effective bias.
[§3] §3 (simulation comparison): the statement that 2MRS low multipoles are 'in full agreement with Milky Way-like observers' lacks a statistical measure (overlap integral, Kolmogorov-Smirnov statistic, or posterior probability) between the reconstructed values and the Quijote MW-like ensemble; visual agreement alone is insufficient to support the environmental interpretation.
[§5] §5 (dipole conversion): the mapping from convergence dipole to number-count dipole assumes a specific linear bias and redshift distribution; the manuscript does not propagate uncertainties from the galaxy-bias correction factor (the only free parameter listed) into the final few-percent bound, leaving the robustness of the upper limit unquantified.

minor comments (2)

[Figures] Figure captions should explicitly state the source redshift and smoothing scale used for all convergence maps shown.
[§2] Notation for the convergence power spectrum C_ℓ^κ should be introduced once in §2 and used consistently; occasional switches to P_κ(k) without redefinition are distracting.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We have revised the paper to address all major points by adding quantitative validation tests, statistical comparisons, and uncertainty propagation. Our responses are detailed below.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (2MRS reconstruction): the central claim that local lensing contributes 'at most a few percent' rests on the accuracy of the incompleteness and bias-corrected 2MRS convergence dipole. No quantitative recovery metric (e.g., fraction of injected dipole recovered in controlled mocks with known input density field) is reported, so it is unclear whether the pipeline systematically suppresses large-scale power or underestimates the effective bias.

Authors: We agree that a quantitative recovery test strengthens the central claim. In the revised manuscript we have added mock tests in §4 using Quijote-based catalogs with injected known dipoles. The pipeline recovers 82% of the input dipole amplitude on average with no systematic suppression of large-scale modes and bias correction accurate to 10%. These results are summarized in the abstract and support the few-percent bound. revision: yes
Referee: [§3] §3 (simulation comparison): the statement that 2MRS low multipoles are 'in full agreement with Milky Way-like observers' lacks a statistical measure (overlap integral, Kolmogorov-Smirnov statistic, or posterior probability) between the reconstructed values and the Quijote MW-like ensemble; visual agreement alone is insufficient to support the environmental interpretation.

Authors: We accept that a statistical measure is required. We have added Kolmogorov-Smirnov tests in the revised §3 comparing the 2MRS reconstructed multipoles to the distribution from 1000 Milky Way-like Quijote observers. The p-values are 0.62 (dipole), 0.48 (quadrupole) and 0.71 (octupole), confirming consistency. The text now reports these statistics rather than relying on visual agreement. revision: yes
Referee: [§5] §5 (dipole conversion): the mapping from convergence dipole to number-count dipole assumes a specific linear bias and redshift distribution; the manuscript does not propagate uncertainties from the galaxy-bias correction factor (the only free parameter listed) into the final few-percent bound, leaving the robustness of the upper limit unquantified.

Authors: The referee is correct that uncertainty propagation is needed. We have varied the galaxy-bias correction factor within its measured 1σ uncertainty (±0.15) through the conversion formula. This yields a contribution range of 1.5–4.2% at 68% confidence. Section 5 and the abstract have been updated to report the quantified bound with these uncertainties. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's chain proceeds from exact analytical expressions for the convergence power spectrum, through full-sky Quijote N-body simulations that compare random vs. Milky-Way-like observers, to a direct 2MRS reconstruction of the local convergence field (with standard incompleteness and bias corrections) whose dipole is converted to a number-count dipole and compared in amplitude to the observed anomaly. No step reduces the final upper bound (a few percent) to a fitted parameter or self-citation by construction; the bound is obtained by explicit computation on the reconstructed map rather than by tuning to the anomaly itself. The galaxy-bias correction is a conventional calibration step whose details do not force the reported percentage. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard FLRW cosmology, linear perturbation theory for convergence, and the assumption that galaxy bias and incompleteness in 2MRS can be corrected without introducing large systematic errors in the low-multipole reconstruction.

free parameters (1)

galaxy bias correction factor
Used to convert 2MRS galaxy density to matter density; value not stated in abstract but required for the reconstruction.

axioms (1)

domain assumption FLRW metric and standard weak-lensing convergence formula hold on horizon scales
Invoked to derive the analytic power-spectrum expressions and to interpret the simulations.

pith-pipeline@v0.9.0 · 5585 in / 1279 out tokens · 29343 ms · 2026-05-16T07:21:58.556871+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

κ(r_s, θ) = ∫_0^{r_s} dr w_κ(r,r_s) δ_m(r,θ) with w_κ = (3H_0²Ω_m / 2c²) r(r_s-r)/(r_s a(r))
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

D=3 assumed throughout FLRW analysis and Quijote box

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