Pith. sign in

REVIEW 1 major objections 4 minor 4 cited by

Velocity Reconstruction from KSZ: Measuring $f_{NL}$ with ACT and DESILS

T0 review · 1 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A kSZ quadratic estimator, extended to photometric galaxy surveys, reconstructs the three-dimensional cosmic velocity field and detects the galaxy-velocity cross-power spectrum at 11.7σ, yielding fNL = -39 +40/-33.

desk verdict The first 3D kSZ velocity reconstruction from a photometric survey, with a careful pipeline and a real but addressable caveat: the covariance underlying the headline SNR and fNL error bars is validated only indirectly. read the letter →

arxiv 2506.21657 v1 pith:YEBPPUJN submitted 2025-06-26 astro-ph.CO

Selim C. Hotinli , Kendrick M. Smith , Simone Ferraro This is my paper
classification astro-ph.CO PACS 98.80.-k98.80.Es
keywords kSZeffectvelocityreconstructionprimordialnon-Gaussianityphotometricredshiftsgalaxy-velocitycross-powerspectrumsurrogatefieldsCMBforegroundsACTDR5
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 claims that the kinetic Sunyaev-Zel'dovich (kSZ) effect can reconstruct the three-dimensional large-scale velocity field using only a photometric galaxy survey, and it demonstrates this with DESI Legacy Imaging Survey LRGs and ACT DR5 CMB maps. It detects the correlation between the reconstructed velocity field and the galaxy density at 11.7σ, the first such detection with photometric redshifts. The measured galaxy-velocity cross-power spectrum implies the galaxy-electron power spectrum is only about 45 percent of a standard halo-model prediction, consistent with strong feedback in gas profiles. Using the measured Pgv(k), the paper places the tightest current fNL constraint from kSZ velocity reconstruction, fNL = -39 +40/-33, consistent with a Gaussian Universe.

What carries the argument

The central machinery is the kSZ quadratic estimator $\hat{v}_r(\mathbf{x}) = \sum_i W_i^v \tilde{T}(\theta_i) \delta^3(\mathbf{x} - \mathbf{x}_i)$, which reconstructs the large-scale radial velocity by summing per-galaxy filtered CMB temperatures, together with surrogate fields: simplified random fields that reproduce the exact field-level covariance of the galaxy density and velocity reconstruction, including survey geometry, photometric redshift scatter, and kSZ reconstruction noise. The surrogate fields allow the paper to compute model predictions and covariances for $P_{gv}(k)$ without realistic DESILS mocks. A mean-subtraction step within redshift bins removes CMB foregrounds correlated with galaxies, and matching the 90 and 150 GHz filters makes the (90 minus 150) null spectrum kSZ-free.

What would settle it

Running the same pipeline on a large suite of full N-body mocks with photometric redshift scatter and realistic CMB foregrounds and noise would give an independent Pgv(k) covariance; if the significance or fNL error bar changes substantially, the surrogate error model is wrong.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that a quadratic estimator originally designed for spectroscopic surveys can be extended to photometric redshifts, where each galaxy is placed at its observed rather than true redshift, and still yield a high-significance galaxy-velocity cross-power spectrum Pgv(k). The estimator v̂r(x) adds to each galaxy a filtered CMB temperature at its position; the paper shows with surrogate-field Monte Carlos that this recovers the radial velocity field on large scales even with photo-z errors. The data give an 11.7σ detection of Pgv(k), a kSZ velocity bias bv = 0.45, and fNL = -39 +40/-33. The low bv means the actual galaxy-electron power spectrum on kSZ-sensitive scales is roughly half the fiducial halo-model prediction, matching other recent kSZ results.

Load-bearing premise

The results assume that the surrogate simulations, which are only checked against realistic mocks for the galaxy auto-spectrum and not for the galaxy-velocity cross-spectrum, correctly size the error bars on the 11.7-sigma detection and the fNL constraint.

Editorial extensions

If this is right

  • Photometric galaxy surveys can be used for kSZ velocity reconstruction, opening the technique to the large volumes and low shot noise of surveys like LSST and the full DESILS footprint.
  • Combining Pgg, Pgv, and Pvv spectra will enable sample-variance cancellation and surpass constraints on fNL from galaxy clustering alone.
  • The measured bv = 0.45 indicates the galaxy-electron power spectrum on kSZ-sensitive scales is roughly half the fiducial halo-model prediction, consistent with strong feedback and smoothed gas profiles.
  • The constraint fNL = -39 +40/-33 is the most stringent fNL measurement to date from kSZ velocity-based analyses, though still consistent with zero.
  • CMB foreground contamination can be controlled: the 90-150 GHz difference spectrum is consistent with zero, and the mean-subtraction step removes foregrounds correlated with the galaxy field.

Reading between the lines

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

  • If the surrogate covariance is as accurate as the paper argues, adding the DESILS South with systematics mitigation could roughly double the volume and push the fNL error toward the 20s, making the technique competitive with galaxy-clustering PNG constraints.
  • The per-galaxy weight exp(-sigma_z^2/(alpha(1+z)^2)) suggests a design principle: for photo-z surveys, weight galaxies inversely to their radial smearing; future surveys could tune alpha per redshift slice.
  • The low bv value implies the Battaglia gas profile overpredicts free electrons on kSZ scales; comparing the same measurement against simulations with varied feedback would map bv to physical gas physics.
  • The night-map null PTE of 0.996 is suspiciously close to 1; tracking whether this repeats with more data is a cheap test of whether the surrogate covariance overestimates errors.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 4 minor

Summary. The paper presents the first three-dimensional kSZ velocity reconstruction using a purely photometric galaxy sample, combining ACT DR5 CMB maps with the DESI Legacy Imaging Surveys LRG catalog restricted to the northern Galactic hemisphere. The authors introduce a quadratic velocity estimator and a 'surrogate field' framework for computing estimator means and covariances without full mocks. They report an 11.7 sigma detection of the galaxy-velocity cross-power spectrum Pgv(k), a velocity bias bv = 0.45^{+0.06}_{-0.05} relative to a fiducial halo-model electron power spectrum, and fNL = -39^{+40}_{-33}. The analysis is supported by null tests based on 90 versus 150 GHz differences, daynight versus night maps, and rotated CMB maps, and by analytic appendices proving the field-level covariance of the surrogate signal and galaxy fields.

Significance. If the central claims hold, this is an important step: it demonstrates that kSZ velocity tomography is feasible with photometric redshifts, opens a new observational route to large-scale velocity fields, and provides one of the strongest current kSZ-based constraints on local primordial non-Gaussianity. The paper is careful in several respects: it provides analytic derivations for the surrogate-field covariance (Appendices B and D), validates the galaxy auto-power covariance against SDSS mocks (Appendix C), runs multiple null tests, checks consistency between independent frequency maps, and makes the analysis code publicly available. These strengths make the paper a serious and credible contribution. The main caveat is that the covariance that sets both the detection significance and the fNL error bars relies on a bootstrap model of the kSZ reconstruction noise that is not directly validated.

major comments (1)
  1. [V C] The reported fNL constraint fixes bg = 2.2 and does not marginalize over its uncertainty, even though the fNL term in Eq. (21) is proportional to (bg - 1). The paper acknowledges this degeneracy but does not quantify the contribution of the fiducial bg uncertainty to the fNL posterior. I recommend profiling over bg or running a joint Pgg + Pgv likelihood to verify that the quoted sigma(fNL) is not underestimated.
minor comments (4)
  1. [III D] In the bullet list following Eq. (32), the phrase 'the noise components Ssig_v(x) are also correlated' should read Snoise_v(x); the label conflates the signal and noise terms.
  2. [Fig. 6] The axis labels in Fig. 6 render as 'P±g±g' and similar; the intended subscripts are Pgg, Pgv90, and Pgv150 and should be corrected for readability.
  3. [V D] The night-map null PTE of 0.996 is noted as 'too good'; the explanation is plausible, but it would be useful to state explicitly that the headline numbers in Eqs. (44)-(46) use the daynight maps, so no correction to those numbers is needed.
  4. [IV A] The text refers to the 98 GHz ACT band as the '90 GHz map'; this convention is stated but should be kept consistent in all figure captions and table headers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured Pgv amplitude and fNL shape constraint are not fixed by the fiducial Pge input or by self-citations; bv is an explicitly marginalized calibration parameter and fNL is fit to the data.

full rationale

The paper's central derivation chain—kSZ quadratic estimator (Eqs. 10–13), Pgv estimator (Eq. 19), and the MCMC likelihood for (bv, fNL) (Eq. 43)—does not reduce by construction to its inputs. The fiducial galaxy-electron spectrum Pge enters the CMB filter Fl (Eq. 10) and the normalization B(x) (Eq. 16), but the overall amplitude is explicitly packaged into the nuisance parameter bv (Eq. 17), which is marginalized in the parameter fit (Sec. V C). Thus the reported bv = 0.45 is a fitted ratio relative to the fiducial halo-model Pge, not a derived consequence of that fiducial model. Similarly, fNL is constrained from the scale-dependent shape of Pgv(k) through the standard local-PNG bias model (Eqs. 5 and 21), and the data return fNL = -39+40/-33, consistent with zero; this is not forced by the surrogate inputs, since the surrogates are used to compute estimator response and covariance while the parameter values come from matching the data bandpowers. The main self-citations ([15], [49], and the hmvec halo-model code) supply the estimator formalism and a fiducial Pge shape, but they are not invoked as a uniqueness theorem, and the reported detection significance depends on the data bandpowers and surrogate covariance rather than collapsing to those citations. The bootstrap reconstruction-noise model (Eq. 32) and the indirect validation of the Pgv covariance are legitimate statistical robustness concerns, but they are not circular reductions of the paper's central results to its inputs; the analysis is self-contained against external data and independent null tests.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim depends on the Gaussianity of large-scale fields, the linear bias and scale-dependent bias model, the halo-model reference P_ge^fid, the photometric redshift error model, and the surrogate field covariance machinery. The main fitted inputs are bv and the fiducial bg; no new physical entities are introduced. The assumptions are stated in the paper, but the Pgv covariance and the halo model reference are the least externally anchored pieces.

free parameters (4)
  • bv (kSZ velocity bias) = 0.45 (+0.06/-0.05) joint
    Nuisance amplitude marginalized in the likelihood; absorbs the ratio between true and fiducial galaxy-electron power spectra (Eq. 17).
  • bg (galaxy bias) = 2.2 (fiducial, from Pgg fit)
    Fixed to a fiducial value to break the degeneracies (bgbv) and (bg-1)bvfNL in Eq. (21); uncertainty in bg is not propagated into the fNL constraint.
  • alpha (photo-z weight exponent) = 0.0025
    Hand-chosen scale in Eq. (39) that down-weights galaxies with large photometric redshift errors; affects the effective survey volume and the velocity reconstruction.
  • CMB filter cutoffs lmin, lmax = 2000, 9000
    Chosen to suppress primary CMB and noise; the filter shape enters F_l in Eq. (38) and therefore the estimator and model predictions.
assumptions (6)
  • domain assumption The large-scale structure fields and the reconstructed velocity field are Gaussian at k < 0.018 Mpc^-1, so power spectrum covariance is captured by the two-point function.
    State in Section III C; used to justify surrogate fields for error bars. Supported by Ref [16] for v-hat-r, but the Pgv covariance itself is not mock-validated.
  • standard math The scale-dependent bias formula in Eq. (5) describes the fNL effect on the galaxy field with delta_c = 1.68 and alpha(k,z) as given.
    Standard result from Dalal et al. and Slosar et al. [31, 32]; it is the basis of the Pgv model in Eq. (21).
  • domain assumption The fiducial galaxy-electron power spectrum P_ge^fid from the hmvec halo model with the Battaglia gas profile is an acceptable reference; the estimator is built on it and bv is defined as the ratio to it.
    Section V C; if the fiducial P_ge is very different, both bv and the fNL response could shift. The paper does not vary the halo model in the analysis.
  • domain assumption The photometric redshift error estimates sigma(z) in the DESILS LRG catalog are unbiased.
    Section IV B; tested indirectly through the Pgg fit in Fig. 4, but a residual bias would distort the velocity reconstruction and Pgv.
  • domain assumption In Appendix D, the normalization proof assumes a snapshot geometry and that the radial velocity is slowly varying on kSZ scales (kS about 1 Mpc^-1).
    This approximation underlies the relation between v-hat-r and the true velocity in Eq. (14) and the surrogate signal field in Eq. (31).
  • domain assumption The 90 and 150 GHz ACT maps are equalized in beam so that the 90-150 difference is kSZ-free (Eq. 36).
    Used to construct the null tests in Section V D; relies on the kSZ signal having a black-body frequency dependence.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Velocity Reconstruction from KSZ: Measuring $f_{NL}$ with ACT and DESILS." pith.science (2026). https://pith.science/paper/YEBPPUJN

@misc{pith2026250621657,
  author       = {Pith},
  title        = {Pith review of: Velocity Reconstruction from KSZ: Measuring $f_NL$ with ACT and DESILS},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YEBPPUJN}},
  note         = {Machine review of arXiv:2506.21657}
}
abstract

The kinetic Sunyaev-Zel'dovich (kSZ) effect offers an indirect way to reconstruct large-scale cosmic velocities, by correlating high-resolution CMB temperature maps with galaxy surveys. In this work, we present the first three-dimensional reconstruction of the large-scale velocity field using a photometric galaxy survey, using data from the DESI Legacy Imaging Surveys (DESILS) and the Atacama Cosmology Telescope (ACT) DR5. We detect an $11.7\sigma$ correlation between our velocity reconstruction and the galaxy field, using only DESILS LRGs in the northern Galactic hemisphere. We find that the overall amplitude of the kSZ-induced correlation is low relative to a halo model prediction ($b_v = 0.45^{+0.06}_{-0.05}$), in agreement with previous results which find high feedback and smoothed gas profiles near massive galaxies. We use this measurement to place new constraints on local-type primordial non-Gaussianity (PNG), obtaining $f_{\rm NL}\!=\!-39^{+40}_{-33}$. This represents the most stringent $f_{\rm NL}$ constraint from kSZ velocity-based analyses to date. We validate our findings through extensive null tests, including tests for CMB foregrounds based on comparing 90 and 150 GHz CMB data.

Figures

Figures reproduced from arXiv: 2506.21657 by the authors.

Figure 1
Figure 1. FIG. 1. Footprint maps of the galaxy and CMB surveys used in this work. The top left panel shows the DESI-LS footprint; [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Histograms of photometric redshifts (left panel) and photo- [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The galaxy power spectrum [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Galaxy-velocity cross-power spectra [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Visualizing the band-power correlations of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Results from our Markov chain Monte Carlo (MCMC) runs using DESI-LS ‘North-only’ patch (see Fig. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Null tests of the galaxy–velocity spectrum difference between 90 and 150 GHz using the DESI-LS ‘North-only’ region [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison between mean power spectra and error bars from SDSS surrogate simulations (blue) and SDSS mocks [PITH_FULL_IMAGE:figures/full_fig_p025_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Comparison between the correlation matrices calculated from SDSS mocks and SDSS surrogate simulations. We find [PITH_FULL_IMAGE:figures/full_fig_p026_10.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Shear-kSZ: A New Estimator for the Matter-Electron Power Spectrum from kSZ Tomography and Weak Lensing

    astro-ph.CO 2026-07 conditional novelty 7.0 of 10

    Shear–kSZ correlates kSZ, tomographic line-of-sight velocity, and lensing convergence to measure P_me(k) and thereby the baryonic matter-power suppression S(k) at high forecast significance.

  2. Optimal and exact wide-angle power spectrum estimation

    astro-ph.CO 2026-07 accept novelty 7.0 of 10

    For finite-rank signals the optimal wide-angle estimator is the two-ℓ Yamamoto form, whose exact window is a finite FFT-computable sum that improves ultra-large-scale SNR by O(1).

  3. Direct shear $\times$ kSZ correlation: controlling baryons without modeling galaxies

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    A shear×velocity kSZ template cross-correlated with the CMB is forecast to measure the electron–matter power spectrum to few-percent (ACT/SO) or sub-percent (CMB-HD) precision.

  4. Constraints on the remote quadrupole field from the polarized Sunyaev Zel'dovich effect

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    A first pSZ bispectrum search with Planck/ACT and unWISE/CIB data finds no signal, giving b_q=1.02±2.64 and τ_rei=−0.01±0.14.

Reference graph

Works this paper leans on

92 extracted references · 11 canonical work pages · cited by 4 Pith papers

  1. [1]

    O. Hahn, R. E. Angulo, and T. Abel, Mon. Not. Roy. Astron. Soc. 454, 3920 (2015), arXiv:1404.2280 [astro-ph.CO]

    arXiv 2015

  2. [2]

    J. Koda, C. Blake, T. Davis, C. Magoulas, C. M. Springob, M. Scrimgeour, A. Johnson, G. B. Poole, and L. Staveley-Smith, Mon. Not. Roy. Astron. Soc. 445, 4267 (2014), arXiv:1312.1022 [astro-ph.CO]

    arXiv 2014

  3. [3]

    J. A. Peacock, Mon. Not. Roy. Astron. Soc. 284, 885 (1997), arXiv:astro-ph/9608151

    work page Pith review arXiv 1997

  4. [4]

    M. A. Strauss and J. A. Willick, Phys. Rept. 261, 271 (1995), arXiv:astro-ph/9502079

    arXiv 1995

  5. [5]

    Bertschinger, in Les Houches Summer School on Cosmology and Large Scale Structure (Session 60)(1993) pp

    E. Bertschinger, in Les Houches Summer School on Cosmology and Large Scale Structure (Session 60)(1993) pp. 273–348, arXiv:astro-ph/9503125

    arXiv 1993

  6. [6]

    H. M. Courtois, A. Dupuy, D. Guinet, G. Baulieu, F. Ruppin, and P. Brenas, Astron. Astrophys. 670, L15 (2023), arXiv:2211.16390 [astro-ph.CO]

    work page Pith review arXiv 2023

  7. [7]

    Jasche and G

    J. Jasche and G. Lavaux, Astron. Astrophys. 625, A64 (2019), arXiv:1806.11117 [astro-ph.CO]

    arXiv 2019

  8. [8]

    K. Said, M. Colless, C. Magoulas, J. R. Lucey, and M. J. Hudson, Mon. Not. Roy. Astron. Soc. 497, 1275 (2020), arXiv:2007.04993 [astro-ph.CO]

    arXiv 2020

Show all 92 references
  1. [9]

    S. S. Boruah, M. J. Hudson, and G. Lavaux, Mon. Not. Roy. Astron. Soc. 498, 2703 (2020), arXiv:1912.09383 [astro- ph.CO]

    2020 arXiv

  2. [10]

    Stiskalek, H

    R. Stiskalek, H. Desmond, J. Devriendt, A. Slyz, G. Lavaux, M. J. Hudson, D. J. Bartlett, and H. M. Courtois, (2025), arXiv:2502.00121 [astro-ph.CO]

    2025

  3. [11]

    R. A. Sunyaev and I. B. Zeldovich, Ann. Rew. of Astron. and Astrophys. 18, 537 (1980)

    1980

  4. [12]

    R. A. Sunyaev and Y. B. Zeldovich, Mon. Not. R. Astron. Soc. 190, 413 (1980)

    1980

  5. [13]

    R. A. Sunyaev and Y. B. Zeldovich, Comments on Astrophysics and Space Physics 2, 66 (1970)

    1970

  6. [14]

    Deutsch, M

    A.-S. Deutsch, M. C. Johnson, M. M¨ unchmeyer, and A. Terrana, J. Cosm. Astropart. Phys. 2018, 034 (2018), arXiv:1705.08907 [astro-ph.CO]

    2018 arXiv

  7. [15]

    K. M. Smith, M. S. Madhavacheril, M. M¨ unchmeyer, S. Ferraro, U. Giri, and M. C. Johnson, arXiv e-prints , arXiv:1810.13423 (2018), arXiv:1810.13423 [astro-ph.CO]

    2018 arXiv

  8. [16]

    Giri and K

    U. Giri and K. M. Smith, arXiv e-prints , arXiv:2010.07193 (2020), arXiv:2010.07193 [astro-ph.CO]

    2020 arXiv

  9. [17]

    Cayuso, R

    J. Cayuso, R. Bloch, S. C. Hotinli, M. C. Johnson, and F. McCarthy, JCAP 02, 051 (2023), arXiv:2111.11526 [astro- ph.CO]

    2023 arXiv

  10. [18]

    M¨ unchmeyer, M

    M. M¨ unchmeyer, M. S. Madhavacheril, S. Ferraro, M. C. Johnson, and K. M. Smith, Phys. Rev. D 100, 083508 (2019), arXiv:1810.13424 [astro-ph.CO]

    2019 arXiv

  11. [19]

    J. I. Cayuso and M. C. Johnson, Phys. Rev. D 101, 123508 (2020), arXiv:1904.10981 [astro-ph.CO]

    2020 arXiv

  12. [20]

    S. C. Hotinli, J. B. Mertens, M. C. Johnson, and M. Kamionkowski, Physical Review D 100, 103528 (2019), arXiv:1908.08953

    2019 arXiv

  13. [21]

    S. C. Hotinli, J. Meyers, N. Dalal, A. H. Jaffe, M. C. Johnson, J. B. Mertens, M. M¨ unchmeyer, K. M. Smith, and A. van Engelen, Phys. Rev. Lett. 123, 061301 (2019), arXiv:1812.03167 [astro-ph.CO]

    2019 arXiv

  14. [22]

    S. C. Hotinli and M. C. Johnson, (2020), arXiv:2012.09851 [astro-ph.CO]

    2020 arXiv

  15. [23]

    S. C. Hotinli, M. C. Johnson, and J. Meyers, Phys. Rev. D 103, 043536 (2021), arXiv:2006.03060 [astro-ph.CO]

    2021 arXiv

  16. [24]

    S. C. Hotinli, K. M. Smith, M. S. Madhavacheril, and M. Kamionkowski, Phys. Rev. D 104, 083529 (2021), arXiv:2108.02207 [astro-ph.CO]

    2021 arXiv

  17. [25]

    Anil Kumar, G

    N. Anil Kumar, G. Sato-Polito, M. Kamionkowski, and S. C. Hotinli, Phys. Rev. D 106, 063533 (2022), arXiv:2205.03423 [astro-ph.CO]

    2022 arXiv

  18. [26]

    N. A. Kumar, S. C. Hotinli, and M. Kamionkowski, Phys. Rev. D 107, 043504 (2023), arXiv:2208.02829 [astro-ph.CO]

    2023 arXiv

  19. [27]

    Komatsu and D

    E. Komatsu and D. N. Spergel, Phys. Rev. D 63, 063002 (2001), arXiv:astro-ph/0005036

    2001 arXiv

  20. [28]

    Verde, L.-M

    L. Verde, L.-M. Wang, A. Heavens, and M. Kamionkowski, Mon. Not. Roy. Astron. Soc. 313, L141 (2000), arXiv:astro- ph/9906301

    2000

  21. [29]

    J. M. Maldacena, JHEP 05, 013 (2003), arXiv:astro-ph/0210603

    2003 arXiv

  22. [30]

    Bartolo, E

    N. Bartolo, E. Komatsu, S. Matarrese, and A. Riotto, Phys. Rept. 402, 103 (2004), arXiv:astro-ph/0406398. 20

    2004 arXiv

  23. [31]

    Dalal, O

    N. Dalal, O. Dore, D. Huterer, and A. Shirokov, Phys. Rev. D 77, 123514 (2008), arXiv:0710.4560 [astro-ph]

    2008 arXiv

  24. [32]

    Slosar, C

    A. Slosar, C. Hirata, U. Seljak, S. Ho, and N. Padmanabhan, JCAP 08, 031 (2008), arXiv:0805.3580 [astro-ph]

    2008 arXiv

  25. [33]

    Aghamousa et al

    A. Aghamousa et al. (DESI), (2016), arXiv:1611.00036 [astro-ph.IM]

    2016 arXiv

  26. [34]

    Abareshi et al

    B. Abareshi et al. (DESI), Astron. J. 164, 207 (2022), arXiv:2205.10939 [astro-ph.IM]

    2022 arXiv

  27. [35]

    Chaussidon et al., (2024), arXiv:2411.17623 [astro-ph.CO]

    E. Chaussidon et al., (2024), arXiv:2411.17623 [astro-ph.CO]

    2024 arXiv

  28. [36]

    Amendola et al., Living Rev

    L. Amendola et al., Living Rev. Rel. 21, 2 (2018), arXiv:1606.00180 [astro-ph.CO]

    2018 arXiv

  29. [37]

    P. A. Abell et al. (LSST Science, LSST Project), (2009), arXiv:0912.0201 [astro-ph.IM]

    2009 arXiv

  30. [38]

    Dor´ eet al

    O. Dor´ eet al. (SPHEREx), (2014), arXiv:1412.4872 [astro-ph.CO]

    2014 arXiv

  31. [39]

    Dor´ eet al

    O. Dor´ eet al. (SPHEREx), (2016), arXiv:1606.07039 [astro-ph.CO]

    2016 arXiv

  32. [40]

    Dor´ eet al

    O. Dor´ eet al. (SPHEREx), (2018), arXiv:1805.05489 [astro-ph.IM]

    2018 arXiv

  33. [41]

    B. P. Crill, M. Werner, et al., in Space Telescopes and Instrumentation 2020: Optical, Infrared, and Millimeter Wave, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 11443, edited by M. Lystrup and M. D. Perrin (2020) p. 114430I, arXiv:2404.11...

    2020 arXiv

  34. [42]

    Akrami et al

    Y. Akrami et al. (Planck), Astron. Astrophys. 641, A9 (2020), arXiv:1905.05697 [astro-ph.CO]

    2020 arXiv

  35. [43]

    Andrews, J

    A. Andrews, J. Jasche, G. Lavaux, and F. Schmidt, Mon. Not. Roy. Astron. Soc. 520, 5746 (2023), arXiv:2203.08838 [astro-ph.CO]

    2023 arXiv

  36. [44]

    D’Amico, Y

    G. D’Amico, Y. Donath, M. Lewandowski, L. Senatore, and P. Zhang, JCAP 05, 059 (2024), arXiv:2206.08327 [astro- ph.CO]

    2024 arXiv

  37. [45]

    D’Amico, M

    G. D’Amico, M. Lewandowski, L. Senatore, and P. Zhang, Phys. Rev. D 111, 063514 (2025), arXiv:2201.11518 [astro- ph.CO]

    2025 arXiv

  38. [46]

    Cabass, M

    G. Cabass, M. M. Ivanov, O. H. E. Philcox, M. Simonovi´ c, and M. Zaldarriaga, Phys. Rev. D 106, 043506 (2022), arXiv:2204.01781 [astro-ph.CO]

    2022 arXiv

  39. [47]

    Rezaie et al

    M. Rezaie et al. (eBOSS), Mon. Not. Roy. Astron. Soc. 506, 3439 (2021), arXiv:2106.13724 [astro-ph.CO]

    2021 arXiv

  40. [48]

    Kurita and M

    T. Kurita and M. Takada, Phys. Rev. D 108, 083533 (2023), arXiv:2302.02925 [astro-ph.CO]

    2023 arXiv

  41. [49]

    Lagu¨ e, M

    A. Lagu¨ e, M. S. Madhavacheril, K. M. Smith, S. Ferraro, and E. Schaan, (2024), arXiv:2411.08240 [astro-ph.CO]

    2024 arXiv

  42. [50]

    Alam et al

    S. Alam et al. (BOSS), Mon. Not. Roy. Astron. Soc. 470, 2617 (2017), arXiv:1607.03155 [astro-ph.CO]

    2017 arXiv

  43. [51]

    K. S. Dawson, D. J. Schlegel, et al., Astron. J. 145, 10 (2013), arXiv:1208.0022 [astro-ph.CO]

    2013 arXiv

  44. [52]

    Naess et al., JCAP 12, 046 (2020), arXiv:2007.07290 [astro-ph.IM]

    S. Naess et al., JCAP 12, 046 (2020), arXiv:2007.07290 [astro-ph.IM]

    2020 arXiv

  45. [53]

    Aghanim et al

    N. Aghanim et al. (Planck), Astron. Astrophys. 641, A1 (2020), arXiv:1807.06205 [astro-ph.CO]

    2020 arXiv

  46. [54]

    McCarthy et al., (2024), arXiv:2410.06229 [astro-ph.CO]

    F. McCarthy et al., (2024), arXiv:2410.06229 [astro-ph.CO]

    2024 arXiv

  47. [55]

    Krywonos, S

    J. Krywonos, S. C. Hotinli, and M. C. Johnson, (2024), arXiv:2408.05264 [astro-ph.CO]

    2024 arXiv

  48. [56]

    Bloch and M

    R. Bloch and M. C. Johnson, (2024), arXiv:2405.00809 [astro-ph.CO]

    2024 arXiv

  49. [57]

    Planck Collaboration, Astronomy & Astrophysics 641, A1 (2020)

    2020

  50. [58]

    Planck Collaboration, Astronomy & Astrophysics 571, A12 (2014), arXiv:arXiv:1303.5072v1

    2014 arXiv

  51. [59]

    E. L. Wright et al., The Astronomical Journal 140, 1868 (2010), arXiv:1008.0031 [astro-ph.IM]

    2010 arXiv

  52. [60]

    Mainzer et al., The Astrophysical Journal 792, 30 (2014), arXiv:1406.6025

    A. Mainzer et al., The Astrophysical Journal 792, 30 (2014), arXiv:1406.6025

    2014 arXiv

  53. [61]

    E. F. Schlafly, A. M. Meisner, and G. M. Green, The Astrophysical Journal Supplement Series 240, 30 (2019)

    2019

  54. [62]

    Krolewski, S

    A. Krolewski, S. Ferraro, E. F. Schlafly, and M. White, Journal of Cosmology and Astroparticle Physics 2020, 047 (2020), arXiv:1909.07412v2

    2020 arXiv

  55. [63]

    A. Dey, D. J. Schlegel, D. Lang, et al., Astron. J. 157, 168 (2019), arXiv:1804.08657 [astro-ph.IM]

    2019 arXiv

  56. [64]

    Coulton et al

    W. Coulton et al. (ACT), Phys. Rev. D 109, 063530 (2024), arXiv:2307.01258 [astro-ph.CO]

    2024 arXiv

  57. [65]

    A. Lai, Y. Kvasiuk, and M. M¨ unchmeyer, KSZ Velocity Reconstruction with ACT and DESI-LS using a Tomographic QML Power Spectrum Estimator (2025)

    2025

  58. [66]

    R. A. Sunyaev and Y. B. Zeldovich, Monthly Notices of the Royal Astronomical Society 190, 413 (1980)

    1980

  59. [67]

    de Mattia and V

    A. de Mattia and V. Ruhlmann-Kleider, JCAP 08, 036 (2019), arXiv:1904.08851 [astro-ph.CO]

    2019 arXiv

  60. [68]

    Scoccimarro, Phys

    R. Scoccimarro, Phys. Rev. D 92, 083532 (2015), arXiv:1506.02729 [astro-ph.CO]

    2015 arXiv

  61. [69]

    N. Hand, Y. Li, Z. Slepian, and U. Seljak, JCAP 07, 002 (2017), arXiv:1704.02357 [astro-ph.CO]

    2017 arXiv

  62. [70]

    Zhou et al

    R. Zhou et al. (DESI), Astron. J. 165, 58 (2023), arXiv:2208.08515 [astro-ph.CO]

    2023 arXiv

  63. [71]

    Zhou et al., JCAP 11, 097 (2023), arXiv:2309.06443 [astro-ph.CO]

    R. Zhou et al., JCAP 11, 097 (2023), arXiv:2309.06443 [astro-ph.CO]

    2023 arXiv

  64. [72]

    White et al., JCAP 02, 007 (2022), arXiv:2111.09898 [astro-ph.CO]

    M. White et al., JCAP 02, 007 (2022), arXiv:2111.09898 [astro-ph.CO]

    2022 arXiv

  65. [73]

    X. Zhou, N. Li, H. Zou, Y. Gong, F. Deng, X. Chen, Q. Yu, Z. He, and B. Ding, Mon. Not. R. Astron. Soc. 536, 2260 (2025), arXiv:2412.02390 [astro-ph.GA]

    2025 arXiv

  66. [74]

    Aghamousa et al

    A. Aghamousa et al. (DESI), (2016), arXiv:1611.00037 [astro-ph.IM]

    2016 arXiv

  67. [75]

    Rezaie et al., Mon

    M. Rezaie et al., Mon. Not. Roy. Astron. Soc. 532, 1902 (2024), arXiv:2307.01753 [astro-ph.CO]

    2024 arXiv

  68. [76]

    Hadzhiyska et al., (2024), arXiv:2407.07152 [astro-ph.CO]

    B. Hadzhiyska et al., (2024), arXiv:2407.07152 [astro-ph.CO]

    2024 arXiv

  69. [77]

    Foreman-Mackey, D

    D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, Publ. Astron. Soc. Pac. 125, 306 (2013), arXiv:1202.3665 [astro-ph.IM]

    2013 arXiv

  70. [78]

    Battaglia, J

    N. Battaglia, J. Cosm. Astropart. Phys. 2016, 058 (2016), arXiv:1607.02442 [astro-ph.CO]

    2016 arXiv

  71. [79]

    Hadzhiyska, S

    B. Hadzhiyska, S. Ferraro, and R. Zhou, Phys. Rev. D 111, 023534 (2025), arXiv:2412.03631 [astro-ph.CO]

    2025 arXiv

  72. [80]

    Ried Guachalla et al., (2025), arXiv:2503.19870 [astro-ph.GA]

    B. Ried Guachalla et al., (2025), arXiv:2503.19870 [astro-ph.GA]

    2025

  73. [81]

    Nelson et al., Comput

    D. Nelson et al., Comput. Astrophys. Cosmol. 6, 2 (2019), arXiv:1812.05609 [astro-ph.GA]. 21

    2019 arXiv

  74. [82]

    Schaye et al., Mon

    J. Schaye et al., Mon. Not. Roy. Astron. Soc. 526, 4978 (2023), arXiv:2306.04024 [astro-ph.CO]. Appendix A: Power spectrum normalization The purpose of this appendix is to explain how the power spectrum normalizations Ngg , Ngv defined in Eq. (19) are computed. We emphasize th...

    2023 arXiv

  75. [84]

    weight function

    Precise statement of theorem It will be convenient to use an abstract notation, where y denotes the vector of parameters associated with each galaxy: y ≡ (θ, ztrue, zobs, σz) (B1) Let xtrue, xobs denote the 3-d locations at sky location θ and redshifts ztrue, zobs respectively...

  76. [85]

    integrating out

    Strategy of proof We define fields eρ(y), eSg(y) on the five-dimensional space y = (θ, ztrue, zobs, σz) by slightly modifying the definitions (B8), (B10) of ρg(x), Sg(x) as follows: eρg(y) ≡ X i∈gal W (yi)δ5(y − yi) − ¯Ng ¯Nr X j∈rand W (yj)δ5(y − yj) eSg(y) ≡ ¯Ng ¯Nr X j∈rand...

  77. [86]

    2-halo” and “1-halo

    Computing ⟨˜ρg(y)˜ρg(y′)⟩ In this section we compute the LHS ⟨eρg(y)eρg(y′)⟩ of Eq. (B14). We will compute the expectation value in two steps. First, we will fix a random realization of δG(y) and compute the expectation value ⟨·⟩pl over random placements of the galaxies {yi}. ...

  78. [87]

    2-halo” and “1-halo

    Computing ⟨ ˜Sg(y) ˜Sg(y′)⟩ In this section we compute the RHS ⟨ eSg(y) eSg(y′)⟩ of Eq. (B14). We write eSg(y) in the form: eSg(y) = X j wjδ5(y − yj) where wj ≡ ¯Ng ¯Nr W (yj) δG(yj) + ηj (B20) We will compute the expectation value ⟨ eSg(y) eSg(y′)⟩ in two steps. First, we wil...

  79. [88]

    main result

    Statement of main result Recall the definition (33) of the velocity reconstruction estimator: ˆvr(x) = X i∈gal W v i eT (θi) δ3(x − xobs i ) (D1) where we have omitted mean-subtraction for simplicity, and assumed photometric redshifts for generality. We are interested in the n...

  80. [89]

    Proof of main result First, we claim that it suffices to prove the main result (D4) in the following special case:

  81. [90]

    (However, we allow WCMB(θ) to be arbitrary, and to have structure on small scales.)

    The galaxy survey does not include an angular mask. (However, we allow WCMB(θ) to be arbitrary, and to have structure on small scales.)

  82. [91]

    The per-galaxy weighting is given by W v i = 1

  83. [92]

    snapshot

    The galaxy catalog is spectroscopic, i.e. σz = 0. To see this, note that if (D4) is true without an angular mask, then it is still true after applying an angular mask on both sides (item #1). Similarly, we can apply a per-galaxy weighting on both sides (item #2), or a photo- z...

  84. [9000]

    extended

    We calculate the power spectra Pge(k), Pgg (k) on the RHS using a halo-model calculation (see §V C for details). The CMB filters F 90 l , F 150 l are shown in Fig. 2. B. DESILS LRG catalogs and processing For the galaxy survey, we use the LRG sample of DESI Legacy Imaging surv...

    2000

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.