Pith. sign in

REVIEW 5 minor 96 references

The optimal ultra-large-scale power-spectrum estimator is a two-multipole Yamamoto generalization with an exact finite FFT window.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.5

2026-07-11 06:31 UTC pith:INWR7YQ5

load-bearing objection Clean, usable advance: finite exact window plus optimality proof for the two-ℓ estimator on finite-rank signals; numerics back the SNR claim on large scales.

arxiv 2607.05513 v1 pith:INWR7YQ5 submitted 2026-07-06 astro-ph.CO

Optimal and exact wide-angle power spectrum estimation

Noah Sailer , Kendrick Smith , Yurii Kvasiuk , Alex Lagu\"e , Selim Hotinli This is my paper
classification astro-ph.CO
keywords wide-angle effectspower spectrum estimatorYamamoto estimatorredshift-space distortionsfinite-rank signalswindow functionkSZ velocity reconstructionultra-large scales
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

On the largest scales the usual plane-parallel power-spectrum estimator is no longer optimal, and its window function has been written only as a slowly converging infinite series. This paper shows that any clustering signal that can be written as a finite sum of rank-1 terms (linear redshift-space distortions, local relativistic contributions, and kSZ radial-velocity reconstruction) has an optimal quadratic estimator whose multipole structure simply matches the signal itself. That estimator is the two-ℓ generalization of Yamamoto already proposed in the literature. The same algebra yields a closed-form expression for the exact window function as a finite sum of survey moments that can be evaluated with ordinary FFTs. For linear RSD the two-ℓ hexadecapole recovers order-unity gains in signal-to-noise on ultra-large scales relative to the conventional single-ℓ estimator.

Core claim

For any finite-rank two-point function the optimal quadratic estimator inherits the same spin structure as the signal, so the two-ℓ estimator with matching multipoles is optimal; its exact window function is the finite angular-momentum sum given in Eq. (3.9) and can be evaluated with O(N_pix log N_pix) FFTs.

What carries the argument

The finite window (Eq. 3.9): a closed sum over Wigner 3j/6j/9j symbols times radial integrals of the generalized survey moments Q_L1L2L3(s), which themselves are FFT-able products of weighted spherical-harmonic transforms of the selection function.

Load-bearing premise

The signals of interest must be finite-rank (or well approximated as such); line-of-sight integrated terms, strong fingers-of-God, and large photometric-redshift smearing are not.

What would settle it

Measure the band-power signal-to-noise of the two-ℓ hexadecapole versus the conventional Yamamoto hexadecapole on the same linear-RSD mocks at k ≲ 10^{-3} h Mpc^{-1}; the claimed order-unity improvement must appear if the finite-rank optimality argument is correct.

Watch this falsifier — get emailed when new claim-graph text bears on it.

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

0 major / 5 minor

Summary. The paper derives the optimal quadratic estimator for finite-rank wide-angle two-point functions and shows that it coincides with the two-ℓ generalization of the Yamamoto estimator (Eq. 1.2) when the estimator multipoles match the signal spins. It further obtains an exact, finite-sum expression for the associated window function (Eq. 3.9) by recoupling four Legendre polynomials with Wigner 3j/9j symbols, and shows that the survey moments Q_{L1 L2 L3}(s) can be evaluated with O(N_pix log N_pix) FFTs (or cheaper Hankel transforms for factorized geometries). The formalism is applied to linear-theory RSD, validated against distant-observer and gSFB expansions (Fig. 2) and against 256 Gaussian realizations (Fig. 3), and is shown to yield order-unity SNR gains for the hexadecapole on ultra-large scales when the (2,2) estimator replaces the conventional (0,4) Yamamoto multipole.

Significance. If the finite-rank assumption holds, the result cleanly solves two long-standing practical problems in wide-angle power-spectrum estimation: optimality of the estimator and exact, non-truncated window functions. The derivation is parameter-free and rests only on standard angular-momentum algebra and the Tegmark quadratic-estimator construction; the numerical tests are pure forward predictions. The claimed O(1) SNR gains on the largest scales are directly relevant for local f_NL and other ultra-large-scale science with DESI, Euclid, SPHEREx and kSZ velocity reconstruction. The explicit finite formulae, recursion relations and full-sky/masked-sky reductions make the method immediately usable.

minor comments (5)
  1. The abstract and introduction emphasize order-unity SNR gains, but Fig. 3 and §5.3 show that those gains are confined to the first few bandpowers (k ≲ few × 10^{-3} h Mpc^{-1}). A single clarifying sentence in the abstract would prevent over-reading the claim.
  2. Eq. (5.5) and Appendix C give the expanded monopole/quadrupole/hexadecapole windows; the text notes that recursion relations reduce the number of independent Q’s, but does not tabulate the final reduced set. A short table or list would aid implementers.
  3. The residual ~1% quadrupole discrepancy between gSFB (ℓ_max=42) and the finite representation at k ≲ 4 imes10^{-4} h Mpc^{-1} (Fig. 2) is mentioned but not diagnosed. A brief remark on whether it is truncation or numerical would be useful.
  4. The 2.8σ mean bias in the 256-GRF comparison (footnote 6) is correctly attributed to discreteness; stating the single-realization equivalent (~0.2σ) already in the main text would reassure readers.
  5. Notation for the radial functions F_i is introduced in Eq. (1.1) and later overloaded with F_RSD_ℓ; a one-line reminder when the RSD specialization begins would help.

Circularity Check

0 steps flagged

No significant circularity: optimality is a standard Tegmark quadratic-estimator application to finite-rank covariances, and the finite window follows from Wigner recoupling with finite selection rules.

full rationale

The paper's two central results are derived independently of data fits and without load-bearing self-citation of the claims themselves. Optimality (§6.1, Eqs. 6.1–6.3) applies Tegmark's external Gaussian quadratic-estimator construction to a rank-1 (or finite-rank) signal covariance: ∂S/∂P_α retains the same Legendre spins as the signal, so the optimal estimator is the two-ℓ form (1.2) with matching multipoles (up to the usual diagonal-weight approximation). The finite window (Eq. 3.9) is obtained by expanding four Legendre polynomials, recoupling via 3j/9j identities (Appendix B.2), and applying the Rayleigh expansion; Wigner triangle conditions make every sum finite by construction for finite spins—not by truncating an infinite series. Numerical checks (Figs. 2–3) are pure forward predictions against GRF simulations and alternative expansions; no parameters are fitted and then re-predicted. Citations to the previously proposed two-ℓ estimator [18, 57] acknowledge prior form, not uniqueness or the optimality/window proofs. Finite-rank scope limitations (integrated terms, strong FoG, large photo-z) are stated explicitly and deferred, not smuggled. The derivation chain is self-contained mathematical reduction under stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The result rests on standard angular-momentum algebra, the definition of finite-rank fields, and the usual Gaussian quadratic-estimator optimality theorem. No free parameters are introduced; the only modeling choices are the classification of which cosmological signals are finite-rank and the diagonal approximation to the inverse covariance (both stated explicitly).

axioms (4)
  • standard math Wigner 3j/6j/9j selection rules and spherical-harmonic addition theorems hold (standard angular-momentum algebra).
    Used throughout Secs. 3, 7 and App. B to reduce the four-Legendre product to a finite sum.
  • domain assumption Linear-theory RSD, local relativistic terms and the Doppler piece of the remote dipole are finite-rank fields (Eqs. 4.1–4.10, 5.1).
    This is the domain of applicability of the finite window; the paper itself notes that integrated terms and strong non-linearities fall outside it.
  • domain assumption For zero-mean Gaussian fields the optimal quadratic estimator is given by the Tegmark formula (Eq. 6.1).
    Standard result from CMB literature; applied without modification to the finite-rank covariance.
  • domain assumption A diagonal (FKP-like) approximation to the inverse covariance is sufficient for the leading optimality statement.
    Stated in Sec. 6.1; multipole leakage is acknowledged but shown numerically to be sub-dominant.

pith-pipeline@v1.1.0-grok45 · 50252 in / 2505 out tokens · 25629 ms · 2026-07-11T06:31:31.183609+00:00 · methodology

0 comments
read the original abstract

What is the optimal power spectrum estimator on ultra-large scales where the plane-parallel approximation breaks down? Conventional estimators, such as the Yamamoto estimator, are only optimal in the plane-parallel limit, while their associated window functions are typically approximated by truncating a slowly converging infinite series. We address two outstanding challenges in the analysis of wide-angle power spectra. First, we derive the optimal estimator for a broad class of clustering signals and show that it is equivalent to a previously proposed two-$\ell$ generalization of the Yamamoto estimator. Second, we show how to write the exact two-$\ell$ window function as a finite number of terms that can be efficiently evaluated using FFTs. Our results apply to a wide range of observables, including redshift-space distortions (RSDs) and large-scale radial-velocity reconstruction from the kinetic Sunyaev-Zel'dovich effect. Focusing on linear-theory RSDs, we validate the finite window-function representation numerically and show that the two-$\ell$ estimator can yield order-unity improvements in the signal-to-noise ratio of ultra-large-scale power spectrum measurements.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

96 extracted references · 81 linked inside Pith

  1. [1]

    Aghamousa, J

    DESI Collaboration, A. Aghamousa, J. Aguilar, S. Ahlen, S. Alam, L.E. Allen et al.,The DESI Experiment Part I: Science,Targeting, and Survey Design,arXiv e-prints(2016) arXiv:1611.00036 [1611.00036]

    Pith/arXiv arXiv 2016

  2. [2]

    Mellier, Abdurro’uf, J.A

    Euclid Collaboration, Y. Mellier, Abdurro’uf, J.A. Acevedo Barroso, A. Achúcarro, J. Adamek et al.,Euclid: I. Overview of the Euclid mission,Astron. Astrophys.697(2025) A1 [2405.13491]

    arXiv 2025

  3. [3]

    Spergel, N

    D. Spergel, N. Gehrels, C. Baltay, D. Bennett, J. Breckinridge, M. Donahue et al.,Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report,arXiv e-prints(2015) arXiv:1503.03757 [1503.03757]. – 22 –

    Pith/arXiv arXiv 2015

  4. [4]

    Mandelbaum, T

    The LSST Dark Energy Science Collaboration, R. Mandelbaum, T. Eifler, R. Hložek, T. Collett, E. Gawiser et al.,The LSST Dark Energy Science Collaboration (DESC) Science Requirements Document,arXiv e-prints(2018) arXiv:1809.01669 [1809.01669]

    Pith/arXiv arXiv 2018

  5. [5]

    Bock, A.M

    J.J. Bock, A.M. Aboobaker, J. Adamo, R. Akeson, J.M. Alred, F. Alibay et al.,The SPHEREx Satellite Mission,arXiv e-prints(2025) arXiv:2511.02985 [2511.02985]

    arXiv 2025

  6. [6]

    Dalal, O

    N. Dalal, O. Doré, D. Huterer and A. Shirokov,Imprints of primordial non-Gaussianities on large-scale structure: Scale-dependent bias and abundance of virialized objects,Phys. Rev. D 77(2008) 123514 [0710.4560]

    Pith/arXiv arXiv 2008

  7. [7]

    Samushia, E

    L. Samushia, E. Branchini and W.J. Percival,Geometric biases in power-spectrum measurements,Mon. Not. R. Astron. Soc.452(2015) 3704 [1504.02135]

    Pith/arXiv arXiv 2015

  8. [8]

    Yoo and U

    J. Yoo and U. Seljak,Wide-angle effects in future galaxy surveys,Mon. Not. R. Astron. Soc. 447(2015) 1789 [1308.1093]

    Pith/arXiv arXiv 2015

  9. [9]

    Reimberg, F

    P.H.F. Reimberg, F. Bernardeau and C. Pitrou,Redshift-space distortions with wide angular separations,JCAP01(2016) 048 [1506.06596]

    Pith/arXiv arXiv 2016

  10. [10]

    Beutler, E

    F. Beutler, E. Castorina and P. Zhang,Interpreting measurements of the anisotropic galaxy power spectrum,JCAP03(2019) 040 [1810.05051]

    Pith/arXiv arXiv 2019

  11. [11]

    Benabou, I

    J.N. Benabou, I. Sands, H.S.G. Gebhardt, C. Heinrich and O. Doré,Wide-angle effects in the power spectrum multipoles in next-generation redshift surveys,Phys. Rev. D110(2024) 083526 [2404.04811]

    Pith/arXiv arXiv 2024

  12. [12]

    Kaiser,Clustering in real space and in redshift space,Mon

    N. Kaiser,Clustering in real space and in redshift space,Mon. Not. R. Astron. Soc.227(1987) 1

    1987

  13. [13]

    Lilje and G

    P.B. Lilje and G. Efstathiou,Gravitationally induced velocity fields in the universe – i. correlation functions,Monthly Notices of the Royal Astronomical Society236(1989) 851 [https://academic.oup.com/mnras/article-pdf/236/4/851/3924694/mnras236-0851.pdf]

    1989

  14. [14]

    Hamilton,Measuring Omega and the Real Correlation Function from the Redshift Correlation Function,Astrophys

    A.J.S. Hamilton,Measuring Omega and the Real Correlation Function from the Redshift Correlation Function,Astrophys. J. Lett.385(1992) L5

    1992

  15. [15]

    McGill,The redshift projection

    C. McGill,The redshift projection. I - Caustics and correlation functions,Mon. Not. R. Astron. Soc.242(1990) 428

    1990

  16. [16]

    Yamamoto, M

    K. Yamamoto, M. Nakamichi, A. Kamino, B.A. Bassett and H. Nishioka,A Measurement of the quadrupole power spectrum in the clustering of the 2dF QSO Survey,Publ. Astron. Soc. Jap.58(2006) 93 [astro-ph/0505115]

    Pith/arXiv arXiv 2006

  17. [17]

    Bianchi, H

    D. Bianchi, H. Gil-Marín, R. Ruggeri and W.J. Percival,Measuring line-of-sight dependent Fourier-space clustering using FFTs,Mon. Not. Roy. Astron. Soc.453(2015) L11 [1505.05341]

    Pith/arXiv arXiv 2015

  18. [18]

    Scoccimarro,Fast Estimators for Redshift-Space Clustering,Phys

    R. Scoccimarro,Fast Estimators for Redshift-Space Clustering,Phys. Rev. D92(2015) 083532 [1506.02729]

    Pith/arXiv arXiv 2015

  19. [19]

    Wilson, J.A

    M.J. Wilson, J.A. Peacock, A.N. Taylor and S. de la Torre,Rapid modelling of the redshift-space power spectrum multipoles for a masked density field,Mon. Not. R. Astron. Soc. 464(2017) 3121 [1511.07799]

    Pith/arXiv arXiv 2017

  20. [20]

    N. Hand, Y. Li, Z. Slepian and U. Seljak,An optimal FFT-based anisotropic power spectrum estimator,JCAP07(2017) 002 [1704.02357]

    Pith/arXiv arXiv 2017

  21. [21]

    Sugiyama, M

    N.S. Sugiyama, M. Shiraishi and T. Okumura,Limits on statistical anisotropy from BOSS DR12 galaxies using bipolar spherical harmonics,Mon. Not. R. Astron. Soc.473(2018) 2737 [1704.02868]

    Pith/arXiv arXiv 2018

  22. [22]

    Hamilton and M

    A.J.S. Hamilton and M. Culhane,Spherical redshift distortions,Mon. Not. Roy. Astron. Soc. 278(1996) 73 [astro-ph/9507021]. – 23 –

    Pith/arXiv arXiv 1996

  23. [23]

    Zaroubi and Y

    S. Zaroubi and Y. Hoffman,Clustering in Redshift Space: Linear Theory,Astrophys. J.462 (1996) 25

    1996

  24. [24]

    Szalay, T

    A.S. Szalay, T. Matsubara and S.D. Landy,Redshift-Space Distortions of the Correlation Function in Wide-Angle Galaxy Surveys,Astrophys. J. Lett.498(1998) L1 [astro-ph/9712007]

    Pith/arXiv arXiv 1998

  25. [25]

    Hamilton,Linear Redshift Distortions: a Review, inThe Evolving Universe, D

    A.J.S. Hamilton,Linear Redshift Distortions: a Review, inThe Evolving Universe, D. Hamilton, ed., vol. 231 ofAstrophysics and Space Science Library, p. 185, Jan., 1998, DOI [astro-ph/9708102]

    Pith/arXiv arXiv 1998

  26. [26]

    Bharadwaj,Radial redshift space distortions,The Astrophysical Journal516(1999) 507

    S. Bharadwaj,Radial redshift space distortions,The Astrophysical Journal516(1999) 507

    1999

  27. [27]

    Fisher, C.A

    K.B. Fisher, C.A. Scharf and O. Lahav,A spherical harmonic approach to redshift distortion and a measurement of Omega(0) from the 1.2-Jy IRAS Redshift Survey,Mon. Not. R. Astron. Soc.266(1994) 219 [astro-ph/9309027]

    Pith/arXiv arXiv 1994

  28. [28]

    Heavens and A.N

    A.F. Heavens and A.N. Taylor,A spherical harmonic analysis of redshift space,Mon. Not. R. Astron. Soc.275(1995) 483 [astro-ph/9409027]

    Pith/arXiv arXiv 1995

  29. [29]

    Gebhardt and O

    H.S.G. Gebhardt and O. Doré,Fabulous code for spherical Fourier-Bessel decomposition,Phys. Rev. D104(2021) 123548 [2102.10079]

    Pith/arXiv arXiv 2021

  30. [30]

    Gebhardt and O

    H.S.G. Gebhardt and O. Doré,Harmonic analysis of isotropic fields on the sphere with arbitrary masks,JCAP01(2022) 038 [2109.13352]

    Pith/arXiv arXiv 2022

  31. [31]

    Grasshorn Gebhardt and O

    H.S. Grasshorn Gebhardt and O. Doré,Validation of spherical Fourier-Bessel power spectrum analysis with log-normal simulations and eBOSS DR16 LRG EZmocks,Phys. Rev. D109 (2024) 083502 [2310.17677]

    Pith/arXiv arXiv 2024

  32. [32]

    Benabou, A

    J.N. Benabou, A. Testa, C. Heinrich, H.S. Grasshorn Gebhardt and O. Doré,Galaxy bispectrum in the spherical Fourier-Bessel basis,Phys. Rev. D109(2024) 103507 [2312.15992]

    Pith/arXiv arXiv 2024

  33. [33]

    Khek, H.G

    B. Khek, H.G. Gebhardt and O. Doré,Fast theoretical predictions for spherical Fourier analysis of large-scale structures,Phys. Rev. D110(2024) 063524 [2212.05760]

    Pith/arXiv arXiv 2024

  34. [34]

    Wen, H.S.G

    R.Y. Wen, H.S.G. Gebhardt, C. Heinrich and O. Doré,Exact Modeling of Power Spectrum Multipole through Spherical Fourier-Bessel Basis,2404.04812

    Pith/arXiv arXiv

  35. [35]

    Wen, H.S.G

    R.Y. Wen, H.S.G. Gebhardt, C. Heinrich and O. Doré,Large-scale Modeling of the Observed Power Spectrum Multipoles,2601.19438

    arXiv

  36. [36]

    Bruton, J.R

    S. Bruton, J.R. Cheshire, O. Doré, H.S.G. Gebhardt and R.Y. Wen,Demonstrating the Use of the Spherical Fourier Bessel Basis for Large Scale Clustering Systematics Discovery and Mitigation with eBOSS,2605.10935

    Pith/arXiv arXiv

  37. [37]

    Castorina and M

    E. Castorina and M. White,Beyond the plane-parallel approximation for redshift surveys,Mon. Not. Roy. Astron. Soc.476(2018) 4403 [1709.09730]

    Pith/arXiv arXiv 2018

  38. [38]

    Szapudi,Wide-Angle Redshift Distortions Revisited,Astrophys

    I. Szapudi,Wide-Angle Redshift Distortions Revisited,Astrophys. J.614(2004) 51 [astro-ph/0404477]

    Pith/arXiv arXiv 2004

  39. [39]

    Pápai and I

    P. Pápai and I. Szapudi,Non-perturbative effects of geometry in wide-angle redshift distortions, Mon. Not. R. Astron. Soc.389(2008) 292 [0802.2940]

    Pith/arXiv arXiv 2008

  40. [40]

    Shaw and A

    J.R. Shaw and A. Lewis,Nonlinear redshift-space power spectra,Phys. Rev. D78(2008) 103512

    2008

  41. [41]

    Raccanelli, L

    A. Raccanelli, L. Samushia and W.J. Percival,Simulating redshift-space distortions for galaxy pairs with wide angular separation,Mon. Not. R. Astron. Soc.409(2010) 1525 [1006.1652]

    Pith/arXiv arXiv 2010

  42. [42]

    Alcock and B

    C. Alcock and B. Paczynski,An evolution free test for non-zero cosmological constant,Nature 281(1979) 358. – 24 –

    1979

  43. [43]

    Matsubara,The Correlation Function in Redshift Space: General Formula with Wide-Angle Effects and Cosmological Distortions,Astrophys

    T. Matsubara,The Correlation Function in Redshift Space: General Formula with Wide-Angle Effects and Cosmological Distortions,Astrophys. J.535(2000) 1 [astro-ph/9908056]

    Pith/arXiv arXiv 2000

  44. [44]

    Shiraishi, K

    M. Shiraishi, K. Akitsu and T. Okumura,Alcock-Paczynski effects on wide-angle galaxy statistics,Phys. Rev. D103(2021) 123534 [2103.08126]

    Pith/arXiv arXiv 2021

  45. [45]

    Yoo, A.L

    J. Yoo, A.L. Fitzpatrick and M. Zaldarriaga,New perspective on galaxy clustering as a cosmological probe: General relativistic effects,Phys. Rev. D80(2009) 083514 [0907.0707]

    Pith/arXiv arXiv 2009

  46. [46]

    Challinor and A

    A. Challinor and A. Lewis,Linear power spectrum of observed source number counts,Phys. Rev. D84(2011) 043516 [1105.5292]

    Pith/arXiv arXiv 2011

  47. [47]

    Bonvin and R

    C. Bonvin and R. Durrer,What galaxy surveys really measure,Phys. Rev. D84(2011) 063505 [1105.5280]

    Pith/arXiv arXiv 2011

  48. [48]

    Beutler and E

    F. Beutler and E. Di Dio,Modeling relativistic contributions to the halo power spectrum dipole, JCAP07(2020) 048 [2004.08014]

    Pith/arXiv arXiv 2020

  49. [49]

    Bertacca, R

    D. Bertacca, R. Maartens, A. Raccanelli and C. Clarkson,Beyond the plane-parallel and Newtonian approach: wide-angle redshift distortions and convergence in general relativity, Journal of Cosmology and Astro-Particle Physics2012(2012) 025 [1205.5221]

    Pith/arXiv arXiv 2012

  50. [50]

    Raccanelli, D

    A. Raccanelli, D. Bertacca, O. Doré and R. Maartens,Large-scale 3D galaxy correlation function and non-Gaussianity,Journal of Cosmology and Astro-Particle Physics2014(2014) 022 [1306.6646]

    Pith/arXiv arXiv 2014

  51. [51]

    Tansella, C

    V. Tansella, C. Bonvin, R. Durrer, B. Ghosh and E. Sellentin,The full-sky relativistic correlation function and power spectrum of galaxy number counts. Part I: theoretical aspects, Journal of Cosmology and Astro-Particle Physics2018(2018) 019 [1708.00492]

    Pith/arXiv arXiv 2018

  52. [52]

    Castorina and E

    E. Castorina and E. di Dio,The observed galaxy power spectrum in General Relativity,JCAP 01(2022) 061 [2106.08857]

    Pith/arXiv arXiv 2022

  53. [53]

    Guedezounme, S

    S.L. Guedezounme, S. Jolicoeur and R. Maartens,Primordial non-Gaussianity — the effects of relativistic and wide-angle corrections to the power spectrum,Journal of Cosmology and Astro-Particle Physics2025(2025) 063 [2412.06553]

    Pith/arXiv arXiv 2025

  54. [54]

    Castorina and M

    E. Castorina and M. White,The Zeldovich approximation and wide-angle redshift-space distortions,Mon. Not. R. Astron. Soc.479(2018) 741 [1803.08185]

    Pith/arXiv arXiv 2018

  55. [55]

    Pardede, E

    K. Pardede, E. Di Dio and E. Castorina,Wide-angle effects in the galaxy bispectrum,Journal of Cosmology and Astro-Particle Physics2023(2023) 030 [2302.12789]

    Pith/arXiv arXiv 2023

  56. [56]

    Castorina and M

    E. Castorina and M. White,Wide angle effects for peculiar velocities,Mon. Not. Roy. Astron. Soc.499(2020) 893 [1911.08353]

    Pith/arXiv arXiv 2020

  57. [57]

    Gil-Marín, J.E

    H. Gil-Marín, J.E. Bautista, R. Paviot, M. Vargas-Magaña, S. de la Torre, S. Fromenteau et al.,The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic power spectrum between redshifts 0.6 and 1.0,Mon. Not. R. Astron. Soc.498 (2020) 24...

    Pith/arXiv arXiv 2020

  58. [58]

    Y. Xie, R. Zhao, G. Gu, X. Wang, X. Mu, Y. Wang et al.,Efficient estimators for power spectrum and bispectrum multipole measurements,arXiv e-prints(2026) arXiv:2605.04864 [2605.04864]

    Pith/arXiv arXiv 2026

  59. [59]

    Feldman, N

    H.A. Feldman, N. Kaiser and J.A. Peacock,Power-Spectrum Analysis of Three-dimensional Redshift Surveys,Astrophys. J.426(1994) 23 [astro-ph/9304022]

    Pith/arXiv arXiv 1994

  60. [60]

    Beutler, H.-J

    F. Beutler, H.-J. Seo, S. Saito, C.-H. Chuang, A.J. Cuesta, D.J. Eisenstein et al.,The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: anisotropic galaxy clustering in Fourier space,Mon. Not. R. Astron. Soc.466(2017) 2242 [1607.03150]. – 25 –

    Pith/arXiv arXiv 2017

  61. [61]

    Hivon, K.M

    E. Hivon, K.M. Górski, C.B. Netterfield, B.P. Crill, S. Prunet and F. Hansen,MASTER of the Cosmic Microwave Background Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex Cosmic Microwave Background Data Sets,Astrophys. J.567 (2002) 2 [astro-ph/0105302]

    Pith/arXiv arXiv 2002

  62. [62]

    Yoo,General relativistic description of the observed galaxy power spectrum: Do we understand what we measure?,Phys

    J. Yoo,General relativistic description of the observed galaxy power spectrum: Do we understand what we measure?,Phys. Rev. D82(2010) 083508 [1009.3021]

    Pith/arXiv arXiv 2010

  63. [63]

    Scaccabarozzi, J

    F. Scaccabarozzi, J. Yoo and S.G. Biern,Galaxy two-point correlation function in general relativity,Journal of Cosmology and Astro-Particle Physics2018(2018) 024 [1807.09796]

    Pith/arXiv arXiv 2018

  64. [64]

    Grimm, F

    N. Grimm, F. Scaccabarozzi, J. Yoo, S.G. Biern and J.-O. Gong,Galaxy power spectrum in general relativity,Journal of Cosmology and Astro-Particle Physics2020(2020) 064 [2005.06484]

    Pith/arXiv arXiv 2020

  65. [65]

    Foglieni, M

    M. Foglieni, M. Pantiri, E. Di Dio and E. Castorina,Large Scale Limit of the Observed Galaxy Power Spectrum,Phys. Rev. Lett.131(2023) 111201 [2303.03142]

    Pith/arXiv arXiv 2023

  66. [66]

    R. Zhou, S. Ferraro, M. White, J. DeRose, N. Sailer, J. Aguilar et al.,DESI luminous red galaxy samples for cross-correlations,Journal of Cosmology and Astro-Particle Physics2023 (2023) 097 [2309.06443]

    Pith/arXiv arXiv 2023

  67. [67]

    Friedman-Shaw, A

    B. Friedman-Shaw, A. Krolewski, M. Foglieni and N. Afshordi,Doppler bias: impact of peculiar velocities on color selection and the large scale structure of galaxy surveys,Journal of Cosmology and Astro-Particle Physics2025(2025) 059 [2410.04705]

    Pith/arXiv arXiv 2025

  68. [68]

    Deutsch, E

    A.-S. Deutsch, E. Dimastrogiovanni, M.C. Johnson, M. Münchmeyer and A. Terrana, Reconstruction of the remote dipole and quadrupole fields from the kinetic Sunyaev Zel’dovich and polarized Sunyaev Zel’dovich effects,Phys. Rev. D98(2018) 123501 [1707.08129]

    Pith/arXiv arXiv 2018

  69. [69]

    Smith, M.S

    K.M. Smith, M.S. Madhavacheril, M. Münchmeyer, S. Ferraro, U. Giri and M.C. Johnson,KSZ tomography and the bispectrum,arXiv e-prints(2018) arXiv:1810.13423 [1810.13423]

    Pith/arXiv arXiv 2018

  70. [70]

    Münchmeyer, M.S

    M. Münchmeyer, M.S. Madhavacheril, S. Ferraro, M.C. Johnson and K.M. Smith,Constraining local non-Gaussianities with kinetic Sunyaev-Zel’dovich tomography,Phys. Rev. D100(2019) 083508 [1810.13424]

    Pith/arXiv arXiv 2019

  71. [71]

    Bloch and M.C

    R. Bloch and M.C. Johnson,Kinetic Sunyaev Zel’dovich velocity reconstruction from Planck and unWISE,arXiv e-prints(2024) arXiv:2405.00809 [2405.00809]

    Pith/arXiv arXiv 2024

  72. [72]

    McCarthy, N

    F. McCarthy, N. Battaglia, R. Bean, J. Richard Bond, H. Cai, E. Calabrese et al.,The Atacama Cosmology Telescope: Large-scale velocity reconstruction with the kinematic Sunyaev-Zel’dovich effect and DESI LRGs,Journal of Cosmology and Astro-Particle Physics 2025(2025) 057 [2410.06229]

    Pith/arXiv arXiv 2025

  73. [73]

    McCarthy, B

    F. McCarthy, B. Hadzhiyska, J.R. Bond, W.R. Coulton, J. Dunkley, C. Embil Villagra et al., The Atacama Cosmology Telescope: Cross-correlation of kSZ and continuity equation velocity reconstruction with photometric DESI LRGs,arXiv e-prints(2025) arXiv:2511.15701 [2511.15701]

    arXiv 2025

  74. [74]

    Laguë, M.S

    A. Laguë, M.S. Madhavacheril, K.M. Smith, S. Ferraro and E. Schaan,Constraints on Local Primordial Non-Gaussianity with 3D Velocity Reconstruction from the Kinetic Sunyaev-Zeldovich Effect,Phys. Rev. Lett.134(2025) 151003 [2411.08240]

    Pith/arXiv arXiv 2025

  75. [75]

    Hotinli, K.M

    S.C. Hotinli, K.M. Smith and S. Ferraro,Velocity Reconstruction from KSZ: MeasuringfN L with ACT and DESILS,arXiv e-prints(2025) arXiv:2506.21657 [2506.21657]

    Pith/arXiv arXiv 2025

  76. [76]

    A.C.M. Lai, Y. Kvasiuk and M. Münchmeyer,KSZ Velocity Reconstruction with ACT and DESI-LS using a Tomographic QML Power Spectrum Estimator,arXiv e-prints(2025) arXiv:2506.21684 [2506.21684]. – 26 –

    Pith/arXiv arXiv 2025

  77. [77]

    Chaussidon, S.C

    E. Chaussidon, S.C. Hotinli, S. Ferraro, K. Smith, X. Chen, J. Aguilar et al.,Measurement of the galaxy-velocity power spectrum of DESI tracers with the kinematic Sunyaev-Zeldovich effect using DESI DR2 and ACT DR6,arXiv e-prints(2026) arXiv:2604.04867 [2604.04867]

    Pith/arXiv arXiv 2026

  78. [78]

    Abitbol, I

    M. Abitbol, I. Abril-Cabezas, S. Adachi, P. Ade, A.E. Adler, P. Agrawal et al.,The Simons Observatory: science goals and forecasts for the enhanced Large Aperture Telescope,Journal of Cosmology and Astro-Particle Physics2025(2025) 034 [2503.00636]

    Pith/arXiv arXiv 2025

  79. [79]

    Terrana, M.-J

    A. Terrana, M.-J. Harris and M.C. Johnson,Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel’dovich effect,Journal of Cosmology and Astro-Particle Physics2017(2017) 040 [1610.06919]

    Pith/arXiv arXiv 2017

  80. [80]

    Ma and E

    C.-P. Ma and E. Bertschinger,Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges,Astrophys. J.455(1995) 7 [astro-ph/9506072]

    Pith/arXiv arXiv 1995

Showing first 80 references.