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arxiv: 2606.08593 · v1 · pith:SRGX3OAMnew · submitted 2026-06-07 · 🌌 astro-ph.CO

Bayesian Reconstruction of the Local Universe from 2MRS: Testing the Gravitational Flow with Cosmicflows-4

Adi Nusser This is my paper

Pith reviewed 2026-06-27 18:09 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Bayesian reconstructionlocal universe2MRSCosmicflows-4peculiar velocitiesZel'dovich approximationgravitational flowredshift survey
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The pith

A Bayesian reconstruction from the 2MRS survey reproduces the gravitational velocities measured by Cosmicflows-4 at the observed galaxy positions.

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

The paper carries out a Bayesian reconstruction of the nearby density and velocity fields using the 2MASS Redshift Survey. It employs a Zel'dovich-approximation forward model with an unbinned Poisson likelihood that accounts for the survey selection function, redshift-space distortions, and a distance-dependent galaxy bias. The maximum-a-posteriori solution and posterior samples are obtained via Hamiltonian Monte Carlo. Direct comparisons at the redshift-space locations of Cosmicflows-4 groups show agreement in object-by-object velocities, density-velocity correlations, and shell-by-shell reflex dipoles without any smoothing of the CF4 data. Evolving the constrained initial conditions with an N-body code preserves the large-scale flow while adding nonlinear small-scale features.

Core claim

The maximum-a-posteriori solution of the Zel'dovich-approximation forward model constrained by the 2MRS redshift-space distribution yields a velocity field that agrees with Cosmicflows-4 peculiar velocities in object-by-object, density-velocity correlation, and shell-by-shell reflex-dipole tests performed at the CF4 redshift-space positions.

What carries the argument

Zel'dovich-approximation forward model with unbinned Poisson point-process likelihood that incorporates the 2MRS selection function, Zone of Avoidance, redshift-space distortions, and distance-dependent galaxy bias.

If this is right

  • The reconstruction captures the large-scale gravitational flow of the nearby Universe.
  • Constrained initial conditions from the reconstruction can be evolved with N-body simulations to develop additional nonlinear small-scale structure while retaining the large-scale Zel'dovich features.
  • The redshift-space distribution in the evolved simulations develops nonlinear Fingers of God.
  • The same framework supplies both the MAP reconstruction and posterior samples for uncertainty quantification.

Where Pith is reading between the lines

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

  • The method could be extended to deeper redshift surveys to map flows on larger scales.
  • Agreement at unsmoothed positions suggests the linear model suffices for velocity reconstruction where CF4 provides dense sampling.
  • The constrained realizations offer a way to test how nonlinear evolution affects inferred initial conditions in future work.

Load-bearing premise

The Zel'dovich approximation combined with the distance-dependent bias prescription and selection function produces an accurate representation of the true gravitational flow at the scales probed by CF4.

What would settle it

A statistically significant mismatch between the reconstructed velocities and the CF4 velocities in the object-by-object comparison at the CF4 redshift-space positions would falsify the agreement claim.

Figures

Figures reproduced from arXiv: 2606.08593 by Adi Nusser.

Figure 1
Figure 1. Figure 1: MDPL2 conditional heat-map tests of the MAP N = 128 radial peculiar-velocity reconstruction. Each panel shows the conditional distribution of the true MDPL2 halo radial velocity at fixed MAP radial velocity. The labels Poisson and normal indicate the likelihood term used in the MAP estimate: an inhomogeneous Poisson point-process likelihood and a Gaussian grid-based likelihood, respectively. The top row sh… view at source ↗
Figure 2
Figure 2. Figure 2: Slice through the Supergalactic plane of the Zel’dovich redshift-space density field. The panels show, from top to bottom, the MAP field, the posterior mean of the evolved HMC fields, and the cell-by-cell posterior me￾dian. All panels show log10(1 + δnl) with the same color scale. White points mark 2MRS galaxies selected to lie close to the plane, |z|/r < 0.05. Redshifts are in the Local Sheet frame. terio… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of projected density maps for one evolved N-body realization and the corresponding Zel’dovich predic￾tion. Each panel shows the SGX–SGY projection through a slab centered on the supergalactic plane with |SGZ| < 15 h −1Mpc. Rows show the N-body and Zel’dovich maps, while columns show real and redshift space. The color scale is the normalized projected density, Σ/⟨Σ⟩. The pixel size in the SGX–SGY… view at source ↗
Figure 4
Figure 4. Figure 4: Projected density of two evolved N-body realizations initialized from independent HMC posterior draws, in su￾pergalactic coordinates. Columns show the two realizations and rows show the SGX–SGY (|SGZ| < 15 h −1Mpc), SGY–SGZ (|SGX| < 15 h −1Mpc), and SGX–SGZ projections. The SGY limits for the bottom row are indicated in the figure. Colors give Σ/⟨Σ⟩ and yellow shading marks the Galactic zone of avoidance, … view at source ↗
Figure 6
Figure 6. Figure 6: Density–radial-velocity correlation, Ψ s δv(r), measured in redshift space with the MAP density field and evaluated for MAP, CF4, and HMC velocity fields at the CF4 positions. Symbols, curves, and uncertainty bands are described in the text. The point-by-point comparison is important, but it does not test whether velocity residuals remain corre￾lated with the reconstructed density field. If the MAP velocit… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between observed CF4 radial pecu￾liar velocities, VCF4, and 2MRS model-predicted radial veloc￾ities, VMAP, for the distance ranges indicated in the panels. The red curve and shaded band show the binned mean and scatter. Dashed lines show the one-to-one relation and the best-fitting linear trend. where η is a zero-mean random contribution at fixed MAP velocity. It represents distance-indicator no… view at source ↗
Figure 7
Figure 7. Figure 7: CF4 shell-by-shell reflex dipole compared with HMC predictions using the same tracer positions, shell se￾lection, and dipole-fitting procedure. Panels show the am￾plitude and Cartesian supergalactic components. CF4 error bars come from Monte Carlo perturbations of the measured radial velocities. Dashed curves show the HMC median, and the grey band gives the central 68% HMC interval for the amplitude. indic… view at source ↗
read the original abstract

We present a Bayesian reconstruction of the local density and velocity fields traced by the 2MASS Redshift Survey (2MRS) and test the inferred gravitational flow against independent Cosmicflows-4 (CF4) galaxy-group peculiar velocities. The fiducial reconstruction is the maximum-a-posteriori (MAP) solution of a Zel'dovich-approximation forward model, constrained by the 2MRS redshift-space distribution through an unbinned Poisson point-process likelihood. The model assumes Gaussian initial conditions and includes the 2MRS selection function, the Zone of Avoidance, redshift-space distortions, and a distance-dependent galaxy-bias prescription. Hamiltonian Monte Carlo provides posterior samples and constrained realizations within the same framework. The reconstructed velocity field agrees well with CF4 in object-by-object, density--velocity-correlation, and shell-by-shell reflex-dipole tests. These comparisons are made at the CF4 redshift-space positions and do not require smoothing the observed CF4 velocities to the MAP resolution. We also evolve constrained initial conditions with Gadget-4. The real-space density retains the large-scale Zel'dovich structure while developing additional nonlinear small-scale structure, and the redshift-space distribution develops nonlinear Fingers of God. The results show that the 2MRS field-level reconstruction captures the large-scale gravitational flow of the nearby Universe and provides initial conditions suitable for constrained simulations.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The paper presents a Bayesian reconstruction of the local density and velocity fields from the 2MRS catalog using a Zel'dovich-approximation (ZA) forward model with an unbinned Poisson point-process likelihood. The fiducial MAP solution incorporates the 2MRS selection function, Zone of Avoidance, redshift-space distortions, and a distance-dependent galaxy-bias prescription. Hamiltonian Monte Carlo sampling yields posterior realizations, and the reconstructed velocity field is tested against independent CF4 peculiar velocities via object-by-object, density-velocity correlation, and shell-by-shell reflex-dipole comparisons performed at the observed CF4 redshift-space positions. Constrained initial conditions are also evolved with Gadget-4 to illustrate nonlinear structure formation.

Significance. If the central claim of accurate capture of the large-scale gravitational flow holds, the work supplies a field-level reconstruction of the nearby universe suitable as initial conditions for constrained N-body simulations. The direct use of unsmoothed CF4 positions for validation and the consistent Bayesian framework (including HMC sampling) are strengths that enhance the result's utility for testing cosmological flows on ~10-100 h^{-1} Mpc scales.

major comments (2)
  1. [Abstract (fiducial reconstruction paragraph)] Abstract (fiducial reconstruction paragraph): the central claim that the ZA forward model (with distance-dependent bias and selection function) produces velocities faithfully representing the true gravitational flow at CF4 scales is load-bearing, yet the manuscript supplies no mock-based quantification of systematic velocity bias or scatter induced by truncation of higher-order Lagrangian terms (v = a f H abla^{-2} abla· abla, omitting dispersion and bulk-flow contributions below ~15-20 h^{-1} Mpc).
  2. [Abstract (tests description)] Abstract (tests description): the reported agreement in object-by-object, density-velocity-correlation, and reflex-dipole tests is presented without quantitative metrics (e.g., Pearson coefficients, rms residuals, or χ^{2} values), error budgets, or details on how the bias prescription and Zone of Avoidance are implemented, preventing verification of the support for the claim that the reconstruction captures the gravitational flow.
minor comments (1)
  1. [Abstract] The notation for the velocity operator in the ZA model is written with spaces around nabla symbols; consistent LaTeX rendering would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each major comment point by point below, providing clarifications and indicating where revisions will be made to improve the presentation.

read point-by-point responses

  1. Referee: [Abstract (fiducial reconstruction paragraph)] Abstract (fiducial reconstruction paragraph): the central claim that the ZA forward model (with distance-dependent bias and selection function) produces velocities faithfully representing the true gravitational flow at CF4 scales is load-bearing, yet the manuscript supplies no mock-based quantification of systematic velocity bias or scatter induced by truncation of higher-order Lagrangian terms (v = a f H abla^{-2} abla· abla, omitting dispersion and bulk-flow contributions below ~15-20 h^{-1} Mpc).

    Authors: We acknowledge that mock-based tests could provide a useful quantification of any systematic velocity bias or scatter arising from the truncation of higher-order terms in the Zel'dovich approximation. Our validation strategy relies instead on direct, unsmoothed comparisons with the independent CF4 dataset across multiple statistics (object-by-object, density-velocity correlation, and reflex dipole), which empirically test whether the reconstructed velocities capture the gravitational flow on the scales probed by CF4. The ZA forward model was selected for its suitability within the Bayesian HMC framework. We agree that a concise discussion of ZA limitations on scales ≾15 h^{-1} Mpc, supported by existing literature, would strengthen the manuscript and will add this in the revised version. revision: partial

  2. Referee: [Abstract (tests description)] Abstract (tests description): the reported agreement in object-by-object, density-velocity-correlation, and reflex-dipole tests is presented without quantitative metrics (e.g., Pearson coefficients, rms residuals, or χ^{2} values), error budgets, or details on how the bias prescription and Zone of Avoidance are implemented, preventing verification of the support for the claim that the reconstruction captures the gravitational flow.

    Authors: The abstract is a high-level summary; the quantitative metrics (Pearson coefficients, rms residuals, and χ^{2} values), error budgets, and full implementation details for the distance-dependent bias prescription and Zone of Avoidance treatment are provided in the methods and results sections of the manuscript. To improve clarity and verifiability, we will revise the abstract to incorporate key quantitative results from the tests and add explicit cross-references to the relevant sections describing the bias model and Zone of Avoidance handling. revision: yes

Circularity Check

0 steps flagged

No circularity: independent CF4 validation on external positions

full rationale

The derivation reconstructs the density/velocity field from 2MRS via a ZA forward model (with selection function and distance-dependent bias) and then compares the resulting velocities to the separate CF4 catalog at CF4 redshift-space positions. These object-by-object, density-velocity, and reflex-dipole tests use data outside the 2MRS likelihood, so agreement is not forced by construction. No self-citations, fitted-input-as-prediction, or ansatz smuggling appear in the load-bearing chain; the model assumptions are stated explicitly and the external test remains falsifiable.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review; ledger populated from stated modeling choices. Gaussian initial conditions and Zel'dovich dynamics are treated as background assumptions. No new particles or forces are introduced.

free parameters (1)
  • distance-dependent galaxy-bias parameters
    Abstract states a distance-dependent galaxy-bias prescription is included; its functional form and any fitted coefficients are not specified.
axioms (2)
  • domain assumption Initial conditions are Gaussian
    Explicitly stated in the model description.
  • domain assumption Zel'dovich approximation suffices for the forward model
    Fiducial reconstruction uses Zel'dovich-approximation forward model.

pith-pipeline@v0.9.1-grok · 5770 in / 1279 out tokens · 18138 ms · 2026-06-27T18:09:00.103034+00:00 · methodology

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Works this paper leans on

58 extracted references · 54 canonical work pages · 1 internal anchor

  1. [1]

    Tully, R. B. 1982, The Astrophysical Journal, 258, 64, doi: 10.1086/160053

    work page doi:10.1086/160053 1982

  2. [2]

    Bilicki, M., Chodorowski, M., Jarrett, T., & Mamon, G. A. 2011, ApJ, 741, 31, doi: 10.1088/0004-637X/741/1/31 20A. Nusser

    work page doi:10.1088/0004-637x/741/1/31 2011

  3. [3]

    Ajhar, E. A. 1999, \apjl, 527, L73, doi: 10.1086/312404

    work page doi:10.1086/312404 1999

  4. [4]

    S., Fiedorowicz, P., & Rozo, E

    Boruah, S. S., Fiedorowicz, P., & Rozo, E. 2024, Physical Review D, 110, 023524, doi: 10.1103/PhysRevD.110.023524

    work page doi:10.1103/physrevd.110.023524 2024

  5. [5]

    , keywords =

    Branchini, E., Davis, M., & Nusser, A. 2012, MNRAS, 424, 472, doi: 10.1111/J.1365-2966.2012.21210.X

    work page doi:10.1111/j.1365-2966.2012.21210.x 2012

  6. [6]

    Classification of halo A-type stars

    Branchini, E., Eldar, A., & Nusser, A. 2002, MNRAS, 335, 53, doi: 10.1046/j.1365-8711.2002.05611.x

    work page doi:10.1046/j.1365-8711.2002.05611.x 2002

  7. [7]

    1993, MNRAS, 264, 375

    Buchert, T., & Ehlers, J. 1993, MNRAS, 264, 375

    1993

  8. [8]

    G., Hoffman, Y., Gottlöber, S., et al

    Carlesi, E., Sorce, J. G., Hoffman, Y., Gottlöber, S., et al. 2016, MNRAS, 458, 900, doi: 10.1093/mnras/stw357

    work page doi:10.1093/mnras/stw357 2016

  9. [9]

    J., Lavaux, G., & Hudson, M

    Carrick, J., Turnbull, S. J., Lavaux, G., & Hudson, M. J. 2015, MNRAS, 450, 317, doi: 10.1093/mnras/stv547

    work page doi:10.1093/mnras/stv547 2015

  10. [10]

    M., Pomarède, D., Tully, R

    Courtois, H. M., Pomarède, D., Tully, R. B., Hoffman, Y., & Courtois, D. 2013, Astronomical Journal, 146, 69, doi: 10.1088/0004-6256/146/3/69 de Grijs, R., & Bono, G. 2020, Astrophysical Journal Supplement Series, 251, 15, doi: 10.3847/1538-4365/abbb96

    work page doi:10.1088/0004-6256/146/3/69 2013

  11. [11]

    , keywords =

    Djorgovski, S., & Davis, M. 1987, ApJ, 313, 59, doi: 10.1086/164948

    work page doi:10.1086/164948 1987

  12. [12]

    1995, MNRAS, 272, 885

    Zaroubi, S. 1995, MNRAS, 272, 885

    1995

  13. [13]

    2002, \nat, 417, 260 Gottlöber, S., Hoffman, Y., & Yepes, G

    Frisch, U., Matarrese, S., Mohayaee, R., & Sobolevski, A. 2002, \nat, 417, 260 Gottlöber, S., Hoffman, Y., & Yepes, G. 2010, in High Performance Computing in Science and Engineering, Garching/Munich 2009, ed. S. Wagner, M. Steinmetz, A. Bode, & M. M. Müller (Berlin, Heidelberg: Springer Berlin Heidelberg), 309–322 Haugbølle, T., Hannestad, S., Thomsen, B....

    work page doi:10.1086/513600 2002

  14. [14]

    Constrained

    Hoffman, Y., & Ribak, E. 1991, ApJL, 380, L5, doi: 10.1086/186160

    work page doi:10.1086/186160 1991

  15. [15]

    P., Macri, L

    Huchra, J. P., Macri, L. M., Masters, K. L., et al. 2012, ApJS, 199, 26, doi: 10.1088/0067-0049/199/2/26

    work page doi:10.1088/0067-0049/199/2/26 2012

  16. [16]

    Jasche, J., & Wandelt, B. D. 2013, MNRAS, 432, 894, doi: 10.1093/mnras/stt449

    work page doi:10.1093/mnras/stt449 2013

  17. [17]

    1987, MNRAS, 227, 1

    Kaiser, N. 1987, MNRAS, 227, 1

    1987

  18. [18]

    D., Makarov, D

    Karachentsev, I. D., Kaisina, E. I., Makarov, D. I., et al. 2013, Astronomical Journal, 145, 101, doi: 10.1088/0004-6256/145/4/101

    work page doi:10.1088/0004-6256/145/4/101 2013

  19. [19]

    2017, MNRAS, 467, 1915, doi: 10.1093/mnras/stx152

    Keselman, A., & Nusser, A. 2017, MNRAS, 467, 1915, doi: 10.1093/mnras/stx152

    work page doi:10.1093/mnras/stx152 2017

  20. [20]

    , keywords =

    Kitaura, F.-S., Erdogdu, P., Nuza, S. E., et al. 2012, MNRAS, 427, L35, doi: 10.1111/j.1745-3933.2012.01330.x

    work page doi:10.1111/j.1745-3933.2012.01330.x 2012

  21. [21]

    2016, MNRAS, 457, 4340, doi: 10.1093/mnras/stw248

    Klypin, A., Yepes, G., Gottlöber, S., Prada, F., & Heß, S. 2016, MNRAS, 457, 4340, doi: 10.1093/mnras/stw248

    work page doi:10.1093/mnras/stw248 2016

  22. [22]

    , keywords =

    Kourkchi, E., Tully, R. B., Eftekharzadeh, S., et al. 2020, ApJ, 902, 145, doi: 10.3847/1538-4357/ABB66B

    work page doi:10.3847/1538-4357/abb66b 2020

  23. [23]

    2016, MNRAS, 455, 3169, doi: 10.1093/mnras/stv2499

    Lavaux, G., & Jasche, J. 2016, MNRAS, 455, 3169, doi: 10.1093/mnras/stv2499

    work page doi:10.1093/mnras/stv2499 2016

  24. [24]

    B., Mohayaee, R., & Colombi, S

    Lavaux, G., Tully, R. B., Mohayaee, R., & Colombi, S. 2010, ApJ, 709, 483, doi: 10.1088/0004-637X/709/1/483

    work page doi:10.1088/0004-637x/709/1/483 2010

  25. [25]

    , keywords =

    Libeskind, N. I., Carlesi, E., Grand, R. J., et al. 2020, MNRAS, 498, 2968, doi: 10.1093/mnras/staa2541

    work page doi:10.1093/mnras/staa2541 2020

  26. [26]

    2024, A&A, 689, A226, doi: 10.1051/0004-6361/202450219

    Lilow, R., Ganeshaiah Veena, P., & Nusser, A. 2024, A&A, 689, A226, doi: 10.1051/0004-6361/202450219

    work page doi:10.1051/0004-6361/202450219 2024

  27. [27]

    2021, MNRAS, 507, 1557, doi: 10.1093/MNRAS/STAB2009

    Lilow, R., & Nusser, A. 2021, MNRAS, 507, 1557, doi: 10.1093/MNRAS/STAB2009

    work page doi:10.1093/mnras/stab2009 2021

  28. [28]

    Linder, E. V. 2005, PRD, 72, 043529, doi: 10.1103/PhysRevD.72.043529

    work page doi:10.1103/physrevd.72.043529 2005

  29. [29]

    M., Kraan-Korteweg, R

    Macri, L. M., Kraan-Korteweg, R. C., Lambert, T., et al. 2019, The Astrophysical Journal Supplement Series, 245, 6, doi: 10.3847/1538-4365/ab465a

    work page doi:10.3847/1538-4365/ab465a 2019

  30. [30]

    P., Côté, P., et al

    Mei, S., Blakeslee, J. P., Côté, P., et al. 2007, Astrophysical Journal, 655, 144, doi: 10.1086/509598

    work page doi:10.1086/509598 2007

  31. [31]

    2025, The Astrophysical Journal, 994, 38, doi: 10.3847/1538-4357/ae17c0

    Mundow, R., & Nusser, A. 2025, The Astrophysical Journal, 994, 38, doi: 10.3847/1538-4357/ae17c0

    work page doi:10.3847/1538-4357/ae17c0 2025

  32. [32]

    2021, Journal of Cosmology and Astroparticle Physics, 2021, 058, doi: 10.1088/1475-7516/2021/03/058

    Nguyen, N.-M., Schmidt, F., Lavaux, G., & Jasche, J. 2021, Journal of Cosmology and Astroparticle Physics, 2021, 058, doi: 10.1088/1475-7516/2021/03/058

    work page doi:10.1088/1475-7516/2021/03/058 2021

  33. [33]

    2023, Physical Review D, 108, 083534, doi: 10.1103/PhysRevD.108.083534

    Mohayaee, R. 2023, Physical Review D, 108, 083534, doi: 10.1103/PhysRevD.108.083534

    work page doi:10.1103/physrevd.108.083534 2023

  34. [34]

    K., Lévy, B., & Mohayaee, R

    Nikakhtar, F., Sheth, R. K., Lévy, B., & Mohayaee, R. 2022, Physical Review Letters, 129, 251101, doi: 10.1103/PhysRevLett.129.251101

    work page doi:10.1103/physrevlett.129.251101 2022

  35. [35]

    2024, Physical Review D, 109, 123512, doi: 10.1103/PhysRevD.109.123512

    Mohayaee, R. 2024, Physical Review D, 109, 123512, doi: 10.1103/PhysRevD.109.123512

    work page doi:10.1103/physrevd.109.123512 2024

  36. [36]

    The panoramic integral-field spectrograph

    Norberg, P., Baugh, C. M., Hawkins, E., et al. 2001, MNRAS, 328, 64, doi: 10.1046/j.1365-8711.2001.04839.x

    work page doi:10.1046/j.1365-8711.2001.04839.x 2001

  37. [37]

    2017, Mon

    Nusser, A. 2017, Mon. Not. R. Astron. Soc. , 470, 445, doi: 10.1093/mnras/stx1225

    work page doi:10.1093/mnras/stx1225 2017

  38. [38]

    , keywords =

    Nusser, A., & Branchini, E. 2000, MNRAS, 313, 587, doi: 10.1046/j.1365-8711.2000.03261.x

    work page doi:10.1046/j.1365-8711.2000.03261.x 2000

  39. [39]

    2011, ApJ, 735, 77, doi: 10.1088/0004-637X/735/2/77

    Nusser, A., Branchini, E., & Davis, M. 2011, ApJ, 735, 77, doi: 10.1088/0004-637X/735/2/77

    work page doi:10.1088/0004-637x/735/2/77 2011

  40. [40]

    1994, ApJL, 421, L1, doi: 10.1086/187172

    Nusser, A., & Davis, M. 1994, ApJL, 421, L1, doi: 10.1086/187172

    work page doi:10.1086/187172 1994

  41. [41]

    2014, ApJ, 788, 157, doi: 10.1088/0004-637X/788/2/157

    Nusser, A., Davis, M., & Branchini, E. 2014, ApJ, 788, 157, doi: 10.1088/0004-637X/788/2/157

    work page doi:10.1088/0004-637x/788/2/157 2014

  42. [42]

    1992, The Astrophysical Journal, 391, 443, doi: 10.1086/171360

    Nusser, A., & Dekel, A. 1992, The Astrophysical Journal, 391, 443, doi: 10.1086/171360

    work page doi:10.1086/171360 1992

  43. [43]

    2020, ApJ, 905, 47, doi: 10.3847/1538-4357/abc42f 2MRS Bayesian Reconstruction21

    Nusser, A., Yepes, G., & Branchini, E. 2020, ApJ, 905, 47, doi: 10.3847/1538-4357/abc42f 2MRS Bayesian Reconstruction21

    work page doi:10.3847/1538-4357/abc42f 2020

  44. [44]

    Peebles, P. J. E. 1980, The large-scale structure of the universe (Princeton University Press, NJ). http://adsabs.harvard.edu/abs/1980lssu.book.....P —. 1989, ApJ, 344, L53, doi: 10.1086/185529

    work page doi:10.1086/185529 1980

  45. [45]

    Peebles, P. J. E., & Tully, R. B. 2013, Astrophysical Journal, 778, 137, doi: 10.1088/0004-637X/778/2/137

    work page doi:10.1088/0004-637x/778/2/137 2013

  46. [46]

    The Astronomical Journal , eprint =

    Riess, A. G., Filippenko, A. V., Challis, P., et al. 1998, AJ, 116, 1009, doi: 10.1086/300499 Rodríguez-Puebla, A., Behroozi, P., Primack, J., et al. 2016, MNRAS, 462, 893, doi: 10.1093/mnras/stw1705

    work page internal anchor Pith review doi:10.1086/300499 1998

  47. [47]

    W., & Chilingarian, I

    Saulder, C., Mieske, S., Zeilinger, W. W., & Chilingarian, I. 2013, AA, 557, A21, doi: 10.1051/0004-6361/201321466

    work page doi:10.1051/0004-6361/201321466 2013

  48. [48]

    2021, Journal of Cosmology and Astroparticle Physics, 2021, 033, doi: 10.1088/1475-7516/2021/04/033

    Schmidt, F. 2021, Journal of Cosmology and Astroparticle Physics, 2021, 033, doi: 10.1088/1475-7516/2021/04/033

    work page doi:10.1088/1475-7516/2021/04/033 2021

  49. [49]

    2024, arXiv e-prints, arXiv:2409.14546

    Scolnic, D., et al. 2024, arXiv e-prints, arXiv:2409.14546. https://arxiv.org/abs/2409.14546

    arXiv 2024

  50. [50]

    2021, Monthly Notices of the Royal Astronomical Society, 506, 2871, doi: 10.1093/mnras/stab1855

    Springel, V., Pakmor, R., Zier, O., & Reinecke, M. 2021, MNRAS, 506, 2871, doi: 10.1093/mnras/stab1855

    work page doi:10.1093/mnras/stab1855 2021

  51. [51]

    B., Rizzi, L., Shaya, E

    Tully, R. B., Rizzi, L., Shaya, E. J., et al. 2009, Astronomical Journal, 138, 323, doi: 10.1088/0004-6256/138/2/323

    work page doi:10.1088/0004-6256/138/2/323 2009

  52. [52]

    B., Shaya, E

    Tully, R. B., Shaya, E. J., Karachentsev, I. D., et al. 2008, ApJ, 676, 184, doi: 10.1086/527428

    work page doi:10.1086/527428 2008

  53. [53]

    ApJ , keywords =

    Tully, R. B., Kourkchi, E., Courtois, H. M., et al. 2023, ApJ, 944, 94, doi: 10.3847/1538-4357/ac94d8

    work page doi:10.3847/1538-4357/ac94d8 2023

  54. [54]

    I., Pomarède, D., et al

    Valade, A., Libeskind, N. I., Pomarède, D., et al. 2024, Nature Astronomy, 8, 1610, doi: 10.1038/s41550-024-02370-0

    work page doi:10.1038/s41550-024-02370-0 2024

  55. [55]

    G., Lilow, R., & Nusser, A

    Veena, P. G., Lilow, R., & Nusser, A. 2023, MNRAS, 522, 5291, doi: 10.1093/mnras/stad1222

    work page doi:10.1093/mnras/stad1222 2023

  56. [56]

    Wempe, E., Lavaux, G., White, S. D. M., et al. 2024, Astronomy & Astrophysics, 691, A348, doi: 10.1051/0004-6361/202450975

    work page doi:10.1051/0004-6361/202450975 2024

  57. [57]

    B., & Lahav, O

    Zaroubi, S., Hoffman, Y., Fisher, K. B., & Lahav, O. 1995, ApJ, 449, 446, doi: 10.1086/176070

    work page doi:10.1086/176070 1995

  58. [58]

    H., et al

    Zehavi, I., Zheng, Z., Weinberg, D. H., et al. 2011, The Astrophysical Journal, 736, 59, doi: 10.1088/0004-637X/736/1/59 Zel’dovich, Y. B. 1970, A&A, 5, 84

    work page doi:10.1088/0004-637x/736/1/59 2011