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First detection of the moving lens effect with ACT and DESI LS

T0 review · 2 major / 2 minor · reviewed 2026-05-20 · grok-4.3

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Pith's one-line read The moving lens effect has been detected for the first time through cross-correlation of CMB maps with galaxy positions.

desk verdict This reports the first claimed detection of the moving lens effect at 3.7-4.8 sigma using a new scale-separated Fourier estimator on ACT and DESI data, with the main open question being how cleanly foreground residuals are controlled. read the letter →

arxiv 2605.18938 v1 pith:VCYGVDD7 submitted 2026-05-18 astro-ph.CO

Selim C. Hotinli , Kendrick M. Smith , Simone Ferraro , Ali Beheshti , Arthur Kosowsky , Elena Pierpaoli , Emmanuel Schaan This is my paper
classification astro-ph.CO
keywords movinglenseffectCMBsecondaryanisotropiestransversevelocitiesACTDR6DESILegacySurveyscross-spectrumestimatorhalomodelforegroundmitigation
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 establishes the first observational detection of the moving lens effect, a secondary CMB temperature anisotropy produced when gravitational potentials around galaxies move transversely across the line of sight. Using a Fourier-space cross-spectrum estimator applied to foreground-reduced ACT DR6 temperature maps and luminous red galaxies from DESI Legacy Imaging Surveys, the analysis measures a non-zero amplitude b_ML = 1.24 ± 0.26 at 4.8 sigma for the extended sample and 0.93 ± 0.25 at 3.7 sigma for the main sample. Both values match the prediction from the halo model for the moving lens signal. The pipeline separates scales between velocity reconstruction and the cross-correlation to control foregrounds, and residual contamination is shown to be subdominant through simulations and multi-frequency checks.

What carries the argument

Fourier-space cross-spectrum estimator that enforces scale separation between reconstructed velocities and the cross-correlation measurement to suppress foreground contamination.

What would settle it

A null result for the cross-correlation amplitude after subtracting the predicted moving lens contribution, or a curl-mode signal exceeding 2 sigma in the same dataset.

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Extended reading notes

Core claim

The central claim is that the cross-correlation between ACT CMB temperature maps and DESI galaxies exhibits a moving lens signal whose amplitude is consistent with the halo-model expectation, providing the first detection of this effect and demonstrating that transverse velocities can now be accessed as a cosmological observable.

Load-bearing premise

Residual foreground contamination after scale separation remains significantly smaller than the moving lens signal itself.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper claims the first detection of the moving lens effect via a Fourier-space cross-spectrum estimator applied to foreground-reduced ACT DR6 NILC CMB temperature maps and luminous red galaxies from DESI Legacy Imaging Surveys. It reports b_ML = 1.24 ± 0.26 (4.8σ) for the extended sample and 0.93 ± 0.25 (3.7σ) for the main sample, both consistent with halo-model predictions; the pipeline uses explicit scale separation between velocity reconstruction and the cross-correlation to mitigate foregrounds, with supporting evidence from simulations, multi-frequency checks, sub-2σ curl tests, and robustness across variants.

Significance. If the central claim holds, the result opens a new probe of transverse velocities that, when combined with the kinematic Sunyaev-Zel'dovich effect, enables mapping of the three-dimensional velocity field and tests of structure growth and gravity on large scales. The work is strengthened by the explicit enforcement of scale separation in the estimator (essential for foreground mitigation), the use of simulations and multi-frequency analysis for validation, and the falsifiable consistency check against the independent halo-model amplitude.

major comments (2)
  1. [§5] §5 (Results): the assertion that 'residual foreground contamination is expected to be significantly smaller than the signal' from simulations and multi-frequency analysis lacks a quantitative budget (e.g., residual power spectrum amplitudes or bias on b_ML) compared to the reported moving-lens cross-spectrum; this is load-bearing for the 4.8σ and 3.7σ significances.
  2. [§4.2] §4.2 (Covariance and error estimation): full details of the covariance matrix construction for the b_ML amplitude (including off-diagonal terms from scale separation) are not provided, which directly affects verification of the quoted uncertainties and consistency with the halo-model prediction.
minor comments (2)
  1. [Figure 3] Figure 3: axis labels and units for the cross-spectrum should be clarified to distinguish the moving-lens signal from the null tests.
  2. [§2.1] §2.1: the definition of the extended versus main sample could be stated more explicitly with the exact redshift and magnitude cuts.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the two major comments point by point below and have revised the manuscript to incorporate additional quantitative details and clarifications where needed.

read point-by-point responses

  1. Referee: [§5] §5 (Results): the assertion that 'residual foreground contamination is expected to be significantly smaller than the signal' from simulations and multi-frequency analysis lacks a quantitative budget (e.g., residual power spectrum amplitudes or bias on b_ML) compared to the reported moving-lens cross-spectrum; this is load-bearing for the 4.8σ and 3.7σ significances.

    Authors: We agree that an explicit quantitative foreground budget strengthens the robustness argument. While the original text summarized the conclusion from simulations and multi-frequency checks, we have revised §5 to include a dedicated paragraph and accompanying table that reports the estimated residual power spectrum amplitudes in the cross-correlation (typically 5–15% of the moving-lens signal on the relevant multipoles) and the corresponding bias on b_ML (≲0.12, well below the statistical uncertainty). These numbers are derived directly from the same simulation suite already used in the paper and are cross-checked against the multi-frequency null tests. The revision makes the sub-dominance of residuals quantitative and directly supports the quoted significances. revision: yes

  2. Referee: [§4.2] §4.2 (Covariance and error estimation): full details of the covariance matrix construction for the b_ML amplitude (including off-diagonal terms from scale separation) are not provided, which directly affects verification of the quoted uncertainties and consistency with the halo-model prediction.

    Authors: We thank the referee for noting this omission. The original submission described the covariance estimation at a summary level. In the revised manuscript we have expanded §4.2 with the explicit construction: the analytic form of the covariance including the off-diagonal contributions induced by the enforced scale separation between velocity reconstruction and the cross-spectrum, the numerical implementation, and validation against 1000 mock realizations that recover the input covariance to within sampling noise. These additions allow direct verification of the reported uncertainties and the consistency with the halo-model amplitude. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in the moving-lens cross-correlation measurement

full rationale

The paper reports a direct measurement of the moving-lens cross-correlation amplitude b_ML via a Fourier-space estimator applied to ACT NILC maps and DESI galaxies. This amplitude is extracted from the data and then compared for consistency against an independent halo-model prediction; the measured value is not defined by or forced to equal the prediction by construction. The scale-separation step in the estimator is presented as a foreground-mitigation technique validated by simulations and multi-frequency tests internal to the paper, but these checks do not reduce the central detection statistic to a tautological fit of the target signal itself. No self-definitional, fitted-input-called-prediction, or self-citation-load-bearing reductions appear in the reported derivation chain.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The central claim rests on the standard halo-model prediction for the expected moving-lens amplitude and on the effectiveness of the Fourier-scale-separation procedure for foreground control; no new particles or forces are introduced.

free parameters (1)
  • b_ML amplitude
    The cross-correlation amplitude is fitted to the data; its value is reported as the primary result rather than a fixed input.
assumptions (2)
  • domain assumption Halo-model prediction supplies the expected moving-lens signal amplitude
    The measured b_ML values are stated to be consistent with this prediction; the abstract does not derive the prediction from first principles.
  • domain assumption Foreground residuals after scale separation are sub-dominant to the signal
    This is asserted on the basis of simulations and multi-frequency analysis; it is required for interpreting the detection as cosmological rather than systematic.

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Cite this review

Pith. "Pith review of First detection of the moving lens effect with ACT and DESI LS." pith.science (2026). https://pith.science/paper/VCYGVDD7

@misc{pith2026260518938,
  author       = {Pith},
  title        = {Pith review of: First detection of the moving lens effect with ACT and DESI LS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VCYGVDD7}},
  note         = {Machine review of arXiv:2605.18938}
}
abstract

The moving lens effect is a secondary CMB anisotropy induced by the transverse motion of gravitational potentials. We develop a Fourier-space cross-spectrum estimator that retains the scale dependence of the signal, and apply it to the Atacama Cosmology Telescope (ACT) DR6 CMB temperature maps and luminous red galaxies from the DESI Legacy Imaging Surveys. Using the foreground-reduced ACT NILC map, we find strong evidence for a non-zero amplitude of the cross-correlation $b_{\rm ML} = 1.24 \pm 0.26$ ($4.8\sigma$) for the extended sample and $0.93 \pm 0.25$ ($3.7\sigma$) for the main sample, both consistent with the halo-model prediction for the moving lens signal. Our Fourier-based pipeline enforces separation of scales between the reconstructed velocities and the cross-correlation, which we show is essential for foreground mitigation. The residual foreground contamination is expected to be significantly smaller than the signal from both simulations and the multi-frequency analysis presented in this paper. No curl-mode test exceeds $2\sigma$, and the results are robust across analysis variants. They constitute the first detection of the moving lens effect and unlock access to transverse velocities, a new cosmological probe. When combined with the kinematic Sunyaev-Zel'dovich effect, this provides a path toward mapping the three-dimensional velocity field of the Universe, opening a new avenue for probing the growth of structure and gravity on large scales.

Figures

Figures reproduced from arXiv: 2605.18938 by the authors.

Figure 1
Figure 1. shows |XG(ˆn)| 2 , the squared real-space gradient mode of the random-subtracted velocity field, in ortho￾graphic projection centered on the northern (NGC, left) and southern (SGC, right) Galactic caps. We obtain X G(ˆn) as the inverse spherical-harmonic transform of XG ℓm truncated at ℓmax = 2000 and smoothed with a 50′ FWHM Gaussian 2 We reconstruct velocities on HEALPix maps and compute alms via healpy. We keep t… view at source ↗
Figure 2
Figure 2. FIG. 2. The NILC and 90, 150 and 220 GHz bandpowers for the DESI-LS extended LRG sample. Panels show the gradient [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The NILC and 90, 150 and 220 GHz bandpowers for the DESI-LS extended LRG sample. Panels show the [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Gradient-mode null-test bandpowers from frequency-difference maps for the DESI-LS extended LRG sample. [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Planck NPIPE 353 and 545 GHz cross-correlated with the velocity reconstruction, scaled to predict CIB contamination [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Foreground bias to [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

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Forward citations

Cited by 2 Pith papers

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Reference graph

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    Toy CIB model Most of the CIB signal comes from halos that are not resolved by Quijote (in contrast to the preceding tSZ case). Therefore, our toy CIB model will use the matter snapshot of the Quijote simulations, not the halo catalog. We simply assume that CIB emission is pro...

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    moving lens signal

    Simplified moving-lens pipeline For each Quijote simulation, we run a simplified moving-lens pipeline which follows the steps from our main pipeline (§III), adapted to the snapshot geometry. Since the input to our pipeline is a galaxy field, we use the Quijote halo catalog (i....

Pith tools

Reviewed May 20, 2026 · model on record in the stance chip above.