Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Template-free BAO method recovers true cosmology in mock survey

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 · deepseek-v4-flash

2026-08-02 23:10 UTC pith:NEKYJNUO

load-bearing objection A careful, incremental but real step in Paranjape & Sheth's template-free BAO program; the headline precision claim is mostly a self-consistency test, but the mathematical machinery is solid and the unbiased f recovery is a genuine improvement. the 3 major comments →

arxiv 2602.14533 v2 pith:NEKYJNUO submitted 2026-02-16 astro-ph.CO

Zel'dovich smearing approximation of the BAO feature for model-agnostic cosmological inference

Aseem Paranjape (IUCAA) , Ravi K. Sheth (UPenn/ICTP) This is my paper
classification astro-ph.CO PACS 98.80.-k98.80.Es
keywords baryon acoustic oscillationsZel'dovich approximationmodel-agnostic inferencecorrelation functiongalaxy clusteringredshift-space distortionsBiSequential basiscosmological parameters
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.

This paper argues that the baryon acoustic oscillation feature can be read as a cosmological standard ruler without ever assuming a specific expanding-universe model. The authors combine the Zel'dovich approximation for how bulk flows smear the BAO peak, a flexible 'BiSequential' basis for the linear-theory shape of the correlation function, and a model for scale-dependent galaxy bias and mode coupling. Using mock observations of a realistic galaxy survey, they report that the true values of the linear point (r_LP), zero-crossing (r_ZC), growth rate f, and velocity dispersion sigma_v are all recovered within 95% confidence, with r_LP and r_ZC at about 0.8% and 1.8% precision and f and sigma_v at roughly 11% precision. If correct, this would let BAO and low-k shape information be interpreted independently of any particular cosmological model, which is especially relevant given current tensions with the standard model.

Core claim

The central discovery is a fully template-free pipeline for BAO inference. The observed multipoles of the galaxy two-point correlation function are written as derivative operators acting on a Gaussian-smeared version of the linear correlation function, following the Zel'dovich approximation. The linear correlation function itself is expanded in the machine-learned BiSequential basis, which the authors show represents the linear correlation function to sub-percent accuracy over 30-150 h^-1 Mpc across a broad class of cosmologies. To pin down the smearing scale, they add measurements of low-k integrals of the power spectrum multipoles, introduced with a free parameter f_v that encodes the frac

What carries the argument

The load-bearing piece is the 'polyLG' version of the Zel'dovich smearing approximation: a Laplace-Gauss expansion in which the redshift-space multipoles of the correlation function are expressed as derivative operators acting on the Gaussian-smoothed linear correlation function, with a single smearing scale sigma. This is coupled to the BiSequential basis, nine basis functions trained to represent the linear correlation function over 30-150 h^-1 Mpc across cosmologies in a 5% neighbourhood of a fiducial model, and to the sdbmc model, which adds scale-dependent bias and a mode-coupling amplitude A_MC. The low-k power spectrum integrals are handled through a free parameter f_v, which absorbs

Load-bearing premise

The BiSequential basis, calibrated on a 5% Latin hypercube of LCDM cosmologies around the best-fit flat model, is assumed to represent the linear two-point correlation function of any true cosmology over 30-150 h^-1 Mpc, even after the derivative operations in the Zel'dovich smearing model amplify any truncation error.

What would settle it

Generate mock survey data from a non-LCDM cosmology, such as one with massive neutrinos summing to 0.5 eV or a dark-energy equation of state w0 = -0.5, and run the same pipeline; if the recovered r_LP or f is not within 95% confidence of the input, the claimed model-agnostic generality is falsified.

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

If this is right

  • If the approach holds, surveys can report BAO distances and growth rates without a fiducial cosmology, making tension checks more direct.
  • The reconstructed linear correlation function encodes more physics than the summary scales r_LP and r_ZC; distances and growth can be extracted jointly from one posterior.
  • The same machinery transfers to Ly-alpha forest and 21cm surveys, since the smearing-bias description is generic.
  • The f_v parameter may itself carry information about the linear velocity power spectrum shape, adding a new observable.
  • Because mode coupling must be modelled, fixing A_MC=0 leads to about a 3-sigma bias in r_LP; future template-based analyses may need similar care.

Where Pith is reading between the lines

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

  • The 'model-agnostic' label is bounded by the calibration of the BiSequential basis around LCDM; cosmologies with very different BAO shapes, such as models with massive neutrinos or exotic dark energy, may require basis augmentation, as the authors note.
  • The tight degeneracy between A_MC and r_LP suggests that any BAO analysis that neglects mode coupling, even template-based ones, risks shifting the inferred peak scale by a comparable amount.
  • A testable extension is to use the f_v posterior to constrain the shape of the primordial velocity power spectrum, potentially breaking degeneracies between sigma_v and bias without external priors.
  • The framework could be applied to real survey data once anisotropic projection effects are added, which the authors state is in preparation.

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

3 major / 5 minor

Summary. The paper assembles a template-free, model-agnostic description of the BAO feature in redshift space. The model combines (i) the sdbmc model of scale-dependent bias and mode coupling from PS25b, (ii) a Zel'dovich-smearing approximation (the polyLG flavour) that recasts the sdbmc integrals as derivative operators acting on a Gaussian-smoothed linear correlation function, and (iii) the machine-learned BiSequential basis of PS25a for the linear-theory correlation function. The framework is tested on toy DESI-like Gaussian mocks and on HADES N-body simulations. The main quantitative claims are unbiased recovery of rLP at ~0.8%, rZC at ~1.8%, and f and sigma_v at ~11% for the toy DESI LRG sample, together with a successful reconstruction of the linear correlation function over 30–150 h^-1 Mpc. The paper is explicit about several limitations, including a weak LCDM prior, the absence of α_parallel/α_perp projection effects, and the lack of power-spectrum integral measurements in the HADES analysis.

Significance. If the claims hold, this would be a valuable step toward BAO inference that does not assume a specific cosmological model for the linear power spectrum shape, going beyond ShapeFit and GSM-EFT in the flexibility of the shape description. The technical development is substantial: the polyLG approximation is derived in detail in Appendix A, compared with an alternative expLG repackaging, and shown to track the exact sdbmc model at ~2% for ell=0,2 and ~30% for ell=4 over the relevant scales. The introduction of f_v as a free parameter in the power-spectrum integrals is an improvement over the ad hoc rescaling in PS23. The HADES comparison provides an independent check on the 2pcf multipole modelling, albeit without the Sigma integrals needed to constrain sigma_v. The main weakness is that the headline unbiased-precision result is a self-consistency test on mocks generated from the same model family that is being approximated, so the transfer of the result to real galaxies or genuinely beyond-LCDM cosmologies is not yet demonstrated.

major comments (3)
  1. [Sec. 3.2, Sec. 4.1, Fig. 1] The primary mock validation is self-referential. The toy DESI mock data have a mean given by the exact sdbmc model of Sec. 2.1 (using PS25b best-fit nuisance parameters), while the fitted model is the polyLG Zel'dovich-smearing approximation to that same sdbmc model, Eqs. (A.41)-(A.46). Fig. 1 therefore mainly demonstrates that polyLG is a good approximation to sdbmc, not that sdbmc+BiSequential describes real galaxy clustering or a cosmology outside the sdbmc family. The HADES analysis in Appendix E is genuinely independent for the 2pcf multipoles, but it lacks the Sigma^(ell)_2 integrals, so sigma_v is essentially unconstrained (Fig. 7) and the unbiased sigma_v/f claims have no independent confirmation. I recommend either adding a validation with N-body or alternative mocks that include measured Sigma integrals, or framing the toy DESI result explicitly as an internal consistency test
  2. [Sec. 2.2, Appendix D, Table 1] The 'model-agnostic' claim is bounded by the calibration and priors. The BiSequential basis was validated on a 5% Latin hypercube of LCDM cosmologies around Planck 2018, and the 'weak LCDM prior' on {w_m} and f_v is a 10x broadening of the scatter in that hypercube. The derivative operators in Eqs. (A.41)-(A.46) involve up to fifth derivatives of smoothed basis functions, which can amplify basis truncation error; the authors themselves note in Sec. 5 that massive neutrinos may require augmenting the basis. Thus, as it stands, the unbiased recovery in Fig. 1 is established only within an LCDM-neighbourhood family. A concrete test would be to generate synthetic observations from a wCDM or massive-neutrino cosmology and check posterior coverage of rLP/rZC/sigma_v, or at least to test the derivative truncation against the exact sdbmc result for a wider range of the basis coefficients.
  3. [Sec. 2.3] The approximate model for the Sigma^(ell)_2 integrals is not bias-free: the text reports an overestimate of ~2.4 sigma for ell=0, ~0.3 sigma for ell=2, and ~0.03 sigma for ell=4 relative to the exact sdbmc integral. Since the toy mocks are generated from the exact integral, the unbiased sigma_v recovery in Fig. 1 relies on this bias being absorbed by the new free parameter f_v and by degeneracies with sigma_v. This is not independently tested because the HADES analysis has no Sigma measurements. I would like to see a test in which the exact sdbmc integral is used in place of the approximate model on the same mocks and the sigma_v posterior is compared, or a simulation-based mock that provides measured Sigma integrals.
minor comments (5)
  1. [Sec. 3.2] The text says the mocks are generated from the exact sdbmc model with PS25b parameter values. I recommend adding an explicit sentence stating that this is a self-consistency test of the polyLG approximation, not an end-to-end validation against independent physics.
  2. [Appendix E, Fig. 7] In the right panel of Fig. 7, the median f is ~0.25 while the stated ground truth is f=0.53. The text says the constraints are 'considerably broader' but does not discuss this apparent ~2-sigma offset. Please comment on whether this is a symptom of the missing Sigma integrals or of the degeneracies with AMC.
  3. [Fig. 1, right panel] The reported chi^2/dof = 96.97/70 with p=0.018 is not a particularly high p-value. Calling the fit 'reasonable' is defensible, but a brief comment on the p-value would help the reader interpret the quality of the model.
  4. [Abstract and Sec. 5] The phrase 'without reference to any particular cosmological model' is stronger than what is implemented: the weak LCDM prior on {w_m} and f_v, and the LCDM-calibrated basis, do encode cosmological assumptions. Suggest rewording to 'without assuming a specific cosmological model for the shape' or similar.
  5. [Appendix D] Minor typo: 'out toy DESI LRG sample' should be 'our toy DESI LRG sample'.

Circularity Check

0 steps flagged

No significant circularity; the headline mock result is a self-consistency/approximation test and the independent HADES check lacks the Sigma integrals, but no prediction reduces to its input by construction.

full rationale

The central derivation is self-contained: Appendix A starts from the exact sdbmc Fourier integrals (Eqs. A.10-A.15), develops the polyLG derivative expansion, and arrives at configuration-space expressions (A.41-A.46) that are then tested against the exact sdbmc calculation (Fig. 5) and against the independent HADES N-body multipoles (Appendix E). The BiSequential basis and sdbmc model are adopted from prior work by the same authors (PS25a, PS25b), but those results are code-reproduced and externally testable; no uniqueness theorem or circular ansatz is invoked. The primary mock validation (Sec. 3.2) generates means from the exact sdbmc model and fits the polyLG approximation to that same model, so Fig. 1 is mainly an internal consistency test of the approximation and sampling pipeline; this is a standard and informative check, not a circular reduction, because the approximate model is not the data generator and can fail (as shown by the biased no-sdbmc and AMC=0 tests in Fig. 4). The main substantive limitations are explicit: the independent HADES analysis lacks the Sigma^(ell)_2 integrals needed to constrain sigma_v (Appendix E; Fig. 7), and Eq. (2.17) treats f_v as a free parameter with a weak LCDM prior derived from the same authors' Latin-hypercube set (Appendix D), so the headline sigma_v precision is prior-assisted and has not been demonstrated outside the sdbmc/LCDM family. These are validation gaps and correctness/caveat concerns, not cases where an output equals an input by construction (f_v is a physical ratio of linear velocity integrals, not a fitted renaming of the measured Sigma). With no exhibited Eq-X=Eq-Y reduction or forced self-citation chain, the circularity score is low.

Axiom & Free-Parameter Ledger

10 free parameters · 7 axioms · 0 invented entities

No new physical particles, forces, or conserved quantities are introduced. The new elements are mathematical: a flexible basis, a repackaged smearing expansion, and nuisance parameters such as f_v and bar-q. The most consequential assumptions are the completeness of the LCDM-calibrated BiSequential basis and the sdbmc model, both inherited from the authors' previous papers.

free parameters (10)
  • sigma_v (linear velocity dispersion) = 3.99^{+0.36}_{-0.53} h^{-1}Mpc (toy DESI)
    Primary cosmological smearing scale; sampled with U[0,12]; controls Gaussian damping in eqs 2.4-2.10.
  • beta = f/b = derived f = 0.677 +/- 0.077 with b ~ 2.43
    Kaiser growth/bias ratio; drives quadrupole and hexadecapole amplitude; sampled U[-1,1].
  • b (Eulerian bias) = 2.43 +/- 0.12
    Large-scale tracer bias; given a 5% Gaussian prior and strongly degenerate with sigma_v.
  • w_0...w_8 (BiSequential basis coefficients) = see Fig. 8 (e.g., w0=0.012+/-0.015, w8=0.0237+/-0.0052)
    Nine coefficients parametrize b^2 xi_lin(r) via eq 2.12; each has a Gaussian 'weak LCDM' prior from PS25a's Latin hypercube.
  • f_v (fractional linear velocity power) = 0.271 +/- 0.050 (prior N(0.26,0.09))
    Free normalization in the Sigma^(ell)_2 model (eq 2.17); constraints are dominated by its Gaussian prior.
  • B1/B1* (scale-dependent density bias) = B1 = 4.4 +/- 1.1 reported
    Sampled as B1* = B1 - sigma^2/(2Rp^2) with uniform prior; shifts the linear point through a Laplacian-like term.
  • Bv/Bv* (scale-dependent velocity bias) = Bv = 3.42^{+1.8}_{-0.73} reported
    Sampled as Bv* = beta Bv; strongly degenerate with sigma_v; input ground truth has a large negative value.
  • sigma (combined smearing scale) = 7.8 +/- 1.2 h^{-1}Mpc
    Defined by sigma^2 = 2(sigma_v^2 + R*^2); sampled separately with hard prior sigma >= sqrt(2) sigma_v.
  • A_MC (mode coupling amplitude) = 0.0155^{+0.0036}_{-0.0088}
    Amplitude of the mode-coupling term (eq 2.3); Gaussian prior N(0,0.05); shows a tight degeneracy with rLP.
  • bar-q^(2) (finite-range constant) = 0.109^{+0.051}_{-0.065}
    Nuisance constant from the s_min truncation of the hexadecapole (eq A.40); uniform prior [-2,2].
axioms (7)
  • domain assumption The sdbmc decomposition xi_NL^(ell) = xi_prop^(ell) + xi_MC^(ell) with eqs (2.1)-(2.5) and B(k,mu) of eq (2.8) is the correct leading-order model of BAO-scale redshift-space clustering.
    Imported from PS25b, not re-derived here; if this model is incomplete for real galaxies, all inferred cosmological parameters inherit the error.
  • domain assumption The Zel'dovich smearing approximation with one Gaussian scale and the O(k^4) polyLG expansion (eqs A.14-A.15) is sufficiently accurate.
    Fig. 5 shows ~2% errors for ell=0,2 and ~30% for ell=4, so the hexadecapole modelling is comparatively fragile.
  • domain assumption The BiSequential basis with M=9 functions spans b^2 xi_lin(r) over 30-150 h^-1 Mpc for all cosmologies of interest.
    The basis was calibrated by PS25a on a 5% LCDM Latin hypercube around Planck 2018; the paper itself notes massive neutrinos may require augmentation.
  • domain assumption The weak LCDM priors on {w_m} and f_v, plus the physical BAO-feature prior, are acceptable for a 'model-agnostic' analysis.
    Section 4.3 states that without these priors the degeneracies produce 'clearly unphysical' fits, so the reported constraints depend on these priors.
  • domain assumption The Gauss-Poisson covariance with propagator-only P(k,mu), ignoring mode coupling, adequately describes the data covariance.
    Appendix C implements this approximation; it is supported only by the authors' earlier convergence tests, not by an independent covariance estimate.
  • domain assumption Fiducial-cosmology projection effects alpha_parallel and alpha_perpendicular can be neglected in this validation.
    Section 3.1 explicitly leaves them to a separate publication; a real DESI data analysis would require them.
  • domain assumption Equation (2.17) is valid: Sigma^(ell)_2 ~ f_v b^2 chi_ell(beta) sigma_v^2 under kmax sigma << 1, with f_v treated as a free parameter.
    The approximation has residual biases of ~4% for ell=0 and ~9% for ell=4, and f_v can absorb part of the mismatch.

pith-pipeline@v1.3.0-alltime-deepseek · 30288 in / 19422 out tokens · 185381 ms · 2026-08-02T23:10:28.014934+00:00 · methodology

0 comments
read the original abstract

A model-agnostic description of the baryon acoustic oscillation (BAO) feature in redshift space requires a number of ingredients. Physically, one must describe the impact of cosmological bulk flows which progressively and anisotropically smear out the feature over time. One must also model the effects of the scale dependence of tracer bias and the mode coupling between short and long scales. All of these can be incorporated using the Zel'dovich approximation alone, without reference to any particular cosmological model. On the technical front, one needs a robust, complete and cosmology-independent basis to describe the shape of the real space BAO feature in linear theory, which can then be propagated to the nonlinearly evolved, measured feature in redshift space. In this work, we describe how these ingredients -- which we have systematically constructed in recent work -- come together in an accurate framework capable of describing the BAO-scale pairwise measurements of state-of-the-art galaxy surveys. Using mock observations and $N$-body simulations, we show that our template-free framework can potentially produce unbiased and precise cosmological constraints for samples with realistic levels of nonlinearity. This work represents one of the final steps towards constructing a data-ready analysis framework for model-agnostic cosmological inference from the BAO feature.

discussion (0)

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

Forward citations

Cited by 1 Pith paper

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

  1. Impact of fiducial cosmology in model-agnostic cosmological inference with the BAO feature

    astro-ph.CO 2026-06 unverdicted novelty 4.0

    The Zel'dovich smearing approximation for model-agnostic BAO inference is extended to include fiducial cosmology distortions and validated on AbacusSummit simulations of DESI- and Euclid-like samples, producing unbias...

Reference graph

Works this paper leans on

47 extracted references · 43 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Eisenstein, I

    D.J. Eisenstein, I. Zehavi, D.W. Hogg, R. Scoccimarro, M.R. Blanton, R.C. Nichol et al., Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies, ApJ633(2005) 560 [astro-ph/0501171]

    Pith/arXiv arXiv 2005

  2. [2]

    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

  3. [3]

    Abdul Karim, J

    M. Abdul Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen, C.A. Prieto et al.,DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints, Phys. Rev. D 112(2025) 083515 [2503.14738]

    Pith/arXiv arXiv 2025

  4. [4]

    d’Amico, J

    G. d’Amico, J. Gleyzes, N. Kokron, K. Markovic, L. Senatore, P. Zhang et al.,The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure, J. Cosmology Astropart. Phys.2020(2020) 005 [1909.05271]

    Pith/arXiv arXiv 2020

  5. [5]

    Ivanov, M

    M.M. Ivanov, M. Simonović and M. Zaldarriaga,Cosmological parameters from the BOSS galaxy power spectrum, J. Cosmology Astropart. Phys.2020(2020) 042 [1909.05277]

    Pith/arXiv arXiv 2020

  6. [7]

    Eggemeier, N

    A. Eggemeier, N. Lee, R. Scoccimarro, B. Camacho-Quevedo, A. Pezzotta, M. Crocce et al., Boosting galaxy clustering analyses with nonperturbative modeling of redshift-space distortions, Phys. Rev. D112(2025) 063532 [2501.18597]

    Pith/arXiv arXiv 2025

  7. [8]

    Ramirez-Solano, M

    S. Ramirez-Solano, M. Icaza-Lizaola, H.E. Noriega, M. Vargas-Magaña, S. Fromenteau, A. Aviles et al.,Full Modeling and parameter compression methods in configuration space for DESI 2024 and beyond, J. Cosmology Astropart. Phys.2025(2025) 129 [2404.07268]

    Pith/arXiv arXiv 2024

  8. [9]

    Brieden, H

    S. Brieden, H. Gil-Marín and L. Verde,ShapeFit: extracting the power spectrum shape information in galaxy surveys beyond BAO and RSD, J. Cosmology Astropart. Phys.2021 (2021) 054 [2106.07641]

    Pith/arXiv arXiv 2021

  9. [10]

    Paranjape and R.K

    A. Paranjape and R.K. Sheth,Model-agnostic cosmological constraints from the baryon acoustic oscillation feature in redshift space, MNRAS (2023) [2304.09198]

    Pith/arXiv arXiv 2023

  10. [11]

    Paranjape and R.K

    A. Paranjape and R.K. Sheth,Model-agnostic basis functions for the 2-point correlation function of dark matter in linear theory, J. Cosmology Astropart. Phys.2025(2025) 009 [2410.21374]

    Pith/arXiv arXiv 2025

  11. [12]

    Paranjape and R.K

    A. Paranjape and R.K. Sheth,Scale-dependent bias and mode coupling in redshift-space clustering near the BAO scale, J. Cosmology Astropart. Phys.2025(2025) 031 [2506.08082]

    Pith/arXiv arXiv 2025

  12. [13]

    Anselmi, G.D

    S. Anselmi, G.D. Starkman and R.K. Sheth,Beating non-linearities: improving the baryon acoustic oscillations with the linear point, MNRAS455(2016) 2474 [1508.01170]. 5http://www.numpy.org 6http://www.scipy.org 7https://matplotlib.org/ 8https://jupyter.org – 14 –

    Pith/arXiv arXiv 2016

  13. [14]

    Anselmi, G.D

    S. Anselmi, G.D. Starkman, P.-S. Corasaniti, R.K. Sheth and I. Zehavi,Galaxy Correlation Functions Provide a More Robust Cosmological Standard Ruler, Phys. Rev. Lett.121(2018) 021302 [1703.01275]

    Pith/arXiv arXiv 2018

  14. [15]

    Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview,arXiv e-prints(2011) arXiv:1104.2932 [1104.2932]

    J. Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview,arXiv e-prints(2011) arXiv:1104.2932 [1104.2932]

    Pith/arXiv arXiv 2011

  15. [16]

    D. Blas, J. Lesgourgues and T. Tram,The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes, J. Cosmology Astropart. Phys.2011(2011) 034 [1104.2933]

    Pith/arXiv arXiv 2011

  16. [17]

    Anselmi, P.-S

    S. Anselmi, P.-S. Corasaniti, G.D. Starkman, R.K. Sheth and I. Zehavi,Linear point standard ruler for galaxy survey data: Validation with mock catalogs, Phys. Rev. D98(2018) 023527 [1711.09063]

    Pith/arXiv arXiv 2018

  17. [18]

    Parimbelli, S

    G. Parimbelli, S. Anselmi, M. Viel, C. Carbone, F. Villaescusa-Navarro, P.S. Corasaniti et al., The effects of massive neutrinos on the linear point of the correlation function, J. Cosmology Astropart. Phys.2021(2021) 009 [2007.10345]

    Pith/arXiv arXiv 2021

  18. [19]

    Nikakhtar, R.K

    F. Nikakhtar, R.K. Sheth and I. Zehavi,Laguerre reconstruction of the correlation function on baryon acoustic oscillation scales, Phys. Rev. D104(2021) 043530 [2101.08376]

    Pith/arXiv arXiv 2021

  19. [20]

    Paranjape and R.K

    A. Paranjape and R.K. Sheth,Bayesian evidence comparison for distance scale estimates, MNRAS517(2022) 4696 [2209.00668]

    Pith/arXiv arXiv 2022

  20. [21]

    Novell-Masot, H

    S. Novell-Masot, H. Gil-Marín, L. Verde, J. Aguilar, S. Ahlen, S. Bailey et al.,Full-Shape analysis of the power spectrum and bispectrum of DESI DR1 LRG and QSO samples, J. Cosmology Astropart. Phys.2025(2025) 005 [2503.09714]

    Pith/arXiv arXiv 2025

  21. [22]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VI. Cosmological parameters,arXiv e-prints(2018) arXiv:1807.06209 [1807.06209]

    Pith/arXiv arXiv 2018

  22. [23]

    Padmanabhan and M

    N. Padmanabhan and M. White,Constraining anisotropic baryon oscillations, Phys. Rev. D77 (2008) 123540 [0804.0799]

    Pith/arXiv arXiv 2008

  23. [24]

    S.-F. Chen, C. Howlett, M. White, P. McDonald, A.J. Ross, H.-J. Seo et al.,Baryon acoustic oscillation theory and modelling systematics for the DESI 2024 results, MNRAS534(2024) 544 [2402.14070]

    Pith/arXiv arXiv 2024

  24. [25]

    Pérez-Fernández, L

    A. Pérez-Fernández, L. Medina-Varela, R. Ruggeri, M. Vargas-Magaña, H. Seo, N. Padmanabhan et al.,Fiducial-cosmology-dependent systematics for the DESI 2024 BAO analysis, J. Cosmology Astropart. Phys.2025(2025) 144 [2406.06085]

    Pith/arXiv arXiv 2024

  25. [26]

    S. Alam, M. Ata, S. Bailey, F. Beutler, D. Bizyaev, J.A. Blazek et al.,The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample, MNRAS470(2017) 2617 [1607.03155]

    Pith/arXiv arXiv 2017

  26. [27]

    Bautista, R

    J.E. Bautista, R. Paviot, M. Vargas Magaña, S. de la Torre, S. Fromenteau, H. Gil-Marín 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 correlation function between redshifts 0.6 and 1, MNRAS500(2021) 736 [2007.08993]

    Pith/arXiv arXiv 2021

  27. [28]

    Villaescusa-Navarro, A

    F. Villaescusa-Navarro, A. Banerjee, N. Dalal, E. Castorina, R. Scoccimarro, R. Angulo et al., The Imprint of Neutrinos on Clustering in Redshift Space, ApJ861(2018) 53 [1708.01154]

    Pith/arXiv arXiv 2018

  28. [29]

    Kirkby, D

    D. Kirkby, D. Margala, A. Slosar, S. Bailey, N.G. Busca, T. Delubac et al.,Fitting methods for baryon acoustic oscillations in the Lyman-αforest fluctuations in BOSS data release 9, J. Cosmology Astropart. Phys.2013(2013) 024 [1301.3456]

    Pith/arXiv arXiv 2013

  29. [30]

    Kärcher, M.-A

    Euclid Collaboration, M. Kärcher, M.-A. Breton, S. de la Torre, A. Veropalumbo, A. Eggemeier et al.,Euclid preparation. Galaxy 2-point correlation function modelling in redshift space,arXiv e-prints(2026) arXiv:2601.04780 [2601.04780]. – 15 –

    arXiv 2026

  30. [31]

    Cobaya: Bayesian analysis in cosmology

    J. Torrado and A. Lewis, “Cobaya: Bayesian analysis in cosmology.” Astrophysics Source Code Library, record ascl:1910.019, Oct., 2019

    1910

  31. [32]

    Torrado and A

    J. Torrado and A. Lewis,Cobaya: code for Bayesian analysis of hierarchical physical models, J. Cosmology Astropart. Phys.2021(2021) 057 [2005.05290]

    Pith/arXiv arXiv 2021

  32. [33]

    Lewis,GetDist: a Python package for analysing Monte Carlo samples,arXiv e-prints(2019) arXiv:1910.13970 [1910.13970]

    A. Lewis,GetDist: a Python package for analysing Monte Carlo samples,arXiv e-prints(2019) arXiv:1910.13970 [1910.13970]

    Pith/arXiv arXiv 2019

  33. [34]

    Lewis,Efficient sampling of fast and slow cosmological parameters, Phys

    A. Lewis,Efficient sampling of fast and slow cosmological parameters, Phys. Rev. D87(2013) 103529 [1304.4473]

    Pith/arXiv arXiv 2013

  34. [35]

    Nikakhtar, R.K

    F. Nikakhtar, R.K. Sheth and I. Zehavi,Laguerre reconstruction of the BAO feature in halo-based mock galaxy catalogues, Phys. Rev. D104(2021) 063504 [2107.12537]

    Pith/arXiv arXiv 2021

  35. [36]

    Baumann, A

    D. Baumann, A. Nicolis, L. Senatore and M. Zaldarriaga,Cosmological non-linearities as an effective fluid, J. Cosmology Astropart. Phys.2012(2012) 051 [1004.2488]

    Pith/arXiv arXiv 2012

  36. [37]

    Carrasco, M.P

    J.J.M. Carrasco, M.P. Hertzberg and L. Senatore,The effective field theory of cosmological large scale structures,Journal of High Energy Physics2012(2012) 82 [1206.2926]

    Pith/arXiv arXiv 2012

  37. [38]

    Crocce and R

    M. Crocce and R. Scoccimarro,Nonlinear evolution of baryon acoustic oscillations, Phys. Rev. D77(2008) 023533 [0704.2783]

    Pith/arXiv arXiv 2008

  38. [39]

    Abdul Karim, J

    M. Abdul Karim, J. Aguilar, S. Ahlen, C. Allende Prieto, O. Alves, A. Anand et al.,DESI DR2 results. I. Baryon acoustic oscillations from the Lyman alpha forest, Phys. Rev. D112 (2025) 083514 [2503.14739]

    Pith/arXiv arXiv 2025

  39. [40]

    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. D77 (2008) 123514 [0710.4560]

    Pith/arXiv arXiv 2008

  40. [41]

    Van Der Walt, S.C

    S. Van Der Walt, S.C. Colbert and G. Varoquaux,The NumPy array: a structure for efficient numerical computation,ArXiv e-prints(2011) [1102.1523]

    Pith/arXiv arXiv 2011

  41. [42]

    Virtanen, R

    P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau et al., SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,Nature Methods17 (2020) 261

    2020

  42. [43]

    Hunter,Matplotlib: A 2d graphics environment,Computing In Science & Engineering9 (2007) 90

    J.D. Hunter,Matplotlib: A 2d graphics environment,Computing In Science & Engineering9 (2007) 90

    2007

  43. [44]

    Grieb, A.G

    J.N. Grieb, A.G. Sánchez, S. Salazar-Albornoz and C. Dalla Vecchia,Gaussian covariance matrices for anisotropic galaxy clustering measurements, MNRAS457(2016) 1577 [1509.04293]

    Pith/arXiv arXiv 2016

  44. [45]

    Chuang, F.-S

    C.-H. Chuang, F.-S. Kitaura, F. Prada, C. Zhao and G. Yepes,EZmocks: extending the Zel’dovich approximation to generate mock galaxy catalogues with accurate clustering statistics, MNRAS446(2015) 2621 [1409.1124]

    Pith/arXiv arXiv 2015

  45. [46]

    Zhao, C.-H

    C. Zhao, C.-H. Chuang, J. Bautista, A. de Mattia, A. Raichoor, A.J. Ross et al.,The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: 1000 multi-tracer mock catalogues with redshift evolution and systematics for galaxies and quasars of the final data release, MNRAS503(2021) 1149 [2007.08997]

    Pith/arXiv arXiv 2021

  46. [47]

    Semenaite, C

    A. Semenaite, C. Blake, A. Porredon, J. Aguilar, S. Ahlen, D. Bianchi et al.,Joint cosmological fits to DESI-DR1 full-shape clustering and weak gravitational lensing in configuration space, arXiv e-prints(2025) arXiv:2512.15961 [2512.15961]

    Pith/arXiv arXiv 2025

  47. [48]

    Nikakhtar, N

    F. Nikakhtar, N. Padmanabhan, B. Lévy, R.K. Sheth and R. Mohayaee,Optimal transport reconstruction of biased tracers in redshift space, Phys. Rev. D108(2023) 083534 [2307.03671]. – 16 – A Zel’dovich smearing details In this Appendix, we describe the development of the Zel’dovich smearing approximation to thesdbmcmodel of PS25b, which we use for our model-...

    Pith/arXiv arXiv 2023