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Fitting five two-point correlations of galaxy density and peculiar velocity in 76,615 local galaxies, this paper measures fσ8(z=0.07)=0.4497±0.0548 and growth index γ_L=0.580±0.110, both consistent with general relativity.

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2026-08-03 18:48 UTC pith:BI5FAU56

load-bearing objection A solid, incremental measurement—first DESI DR1 PV growth rate from correlation functions—with a real gap in validation at the analysis redshift. the 3 major comments →

arxiv 2512.03230 v2 pith:BI5FAU56 submitted 2025-12-02 astro-ph.CO

The DESI DR1 Peculiar Velocity Survey: growth rate measurements from galaxy and momentum correlation functions

R. J. Turner , C. Blake , F. Qin , J. Aguilar , S. Ahlen , A. J. Amsellem , J. Bautista , S. BenZvi
show 56 more authors
D. Bianchi D. Brooks A. Carr E. Chaussidon T. Claybaugh A. Cuceu A. de la Macorra P. Doel K. Douglass S. Ferraro A. Font-Ribera J. E. Forero-Romero E. Gazta\~naga S. Gontcho A Gontcho G. Gutierrez J. Guy H. K. Herrera-Alcantar K. Honscheid C. Howlett D. Huterer M. Ishak R. Joyce R. Kehoe A. G. Kim D. Kirkby A. Kremin O. Lahav Y. Lai C. Lamman M. Landriau L. Le Guillou A. Leauthaud M. E. Levi M. Manera A. Meisner R. Miquel J. Moustakas A. Mu\~noz-Guti\'errez S. Nadathur N. Palanque-Delabrouille W. J. Percival C. Poppett F. Prada I. P\'erez-R\`afols C. Ross G. Rossi K. Said E. Sanchez D. Schlegel M. Schubnell J. Silber D. Sprayberry G. Tarl\'e B. A. Weaver P. Zarrouk H. Zou
This is my paper
classification astro-ph.CO
keywords peculiar velocitiesgrowth rate fσ8momentum correlation functionsDESI DR1Eulerian perturbation theoryTully-Fisher relationFundamental Planegalaxy clustering
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.

The paper sets out to show that the growth rate of cosmic structure can be pinned down from the motions of local galaxies, using the largest peculiar-velocity sample assembled to date: 76,615 velocities from the Fundamental Plane and Tully-Fisher relations, combined with 415,523 galaxy redshifts from the bright galaxy survey. Fitting five two-point correlation statistics with models built from 1-loop Eulerian perturbation theory, it obtains fσ8 = 0.391^{+0.080}_{-0.081} at z_eff = 0.07, and a three-method consensus of fσ8(z=0.07) = 0.4497±0.0548, both consistent with the standard ΛCDM prediction. Combined with full-shape clustering, the gravitational growth index is γ_L = 0.580±0.110, consistent with general relativity. Why this matters: peculiar velocities probe gravity on the large scales where modified-gravity theories would show up before screening, giving an independent low-redshift test of the standard model of gravity.

Core claim

On the paper's own terms: the normalised growth rate fσ8 at z=0.07 is measured by jointly fitting five correlation statistics — the momentum auto-correlations ψ1 and ψ2, the galaxy clustering monopole and quadrupole, and the galaxy-momentum cross-correlation dipole — with non-linear models generated from 1-loop Eulerian perturbation theory. The fiducial five-statistic fit yields fσ8 = 0.391^{+0.080}_{-0.081} (20.6% error), a 37.4% error improvement over clustering-only fits. Combining with the power-spectrum and maximum-likelihood analyses of the same data gives a consensus fσ8(z=0.07) = 0.4497±0.0548, and jointly fitting this with DESI full-shape clustering gives γ_L = 0.580±0.110. Both are

What carries the argument

The central object is the momentum field — the density-weighted peculiar velocity — whose two-point auto-correlation functions ψ1(r), ψ2(r) and cross-correlation with galaxy density carry the growth-rate signal. At leading order the line-of-sight momentum power spectrum is P_pp(k,μ) = (aHfμ/k)^2 P_L(k), so its monopole equals (1/3)P_v(k); that factor of 1/3 is what lets the ψ statistics isolate fσ8. The models are built from 1-loop Eulerian perturbation theory density and momentum power spectra, transformed to configuration space with FFTLog, with two fitted non-linear velocity-dispersion parameters σ²_vT and σ²_vS. The estimators use optimal weights and log-distance ratios η to handle the l

Load-bearing premise

The load-bearing premise is that the 1-loop Eulerian perturbation-theory power spectra, with only two fitted velocity-dispersion parameters, correctly describe these biased galaxies and momentum tracers over 24–120 h⁻¹Mpc at z≈0.07 — models the paper adopts wholesale from a companion paper (§3.1: 'We will not describe in detail how these power spectra models are produced') rather than deriving or validating here.

What would settle it

Run the five-statistic pipeline on N-body mocks built at z≈0.07 (the DR1 effective redshift) rather than the z=0.2 snapshot used here, and check whether the recovered fσ8 distribution centres on the input value within the ~14% mock scatter; a biased recovery would falsify the perturbation-theory modelling. A second check: a >1σ discrepancy between fσ8 from the FP-only and z<0.05 TF-only samples would signal an unmodelled systematics in the velocity calibration.

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

If this is right

  • Peculiar-velocity correlations add real constraining power: adding them to clustering-only fits cuts the fσ8 error by about 37%, and the momentum–galaxy cross-correlation dipole adds a further 5%.
  • The consensus fσ8(z=0.07)=0.4497±0.0548 sits on the ΛCDM prediction (0.444), so DESI DR1 sees no low-redshift growth-rate anomaly.
  • The growth index γ_L=0.580±0.110 is within 1σ of general relativity's 0.55, leaving no evidence for modified gravity in the local velocity field at this precision.
  • The fit is insensitive to the choice of scale range (lower bounds 12–30 h⁻¹Mpc, upper bounds 96–136 h⁻¹Mpc) and recovers the fiducial cosmology of the mocks, supporting the robustness of the central value.

Where Pith is reading between the lines

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

  • Editorial inference: because momentum signal-to-noise grows toward large scales (bulk flows), the error here is dominated by the DR1 sky coverage; completing the footprint in DR2 should improve fσ8 more than the sample-size increase alone suggests.
  • Editorial inference: the unexplained excess TF correlation at z>0.05 — which the paper conservatively cuts — could be checked tomographically; if real, it would appear as a scale-dependent dipole signal and would need to be modelled rather than cut.
  • Editorial inference: the wholesale adoption of the companion paper's power-spectrum models means the fσ8 error budget omits the modelling uncertainty; a direct simulation-based test of the two-parameter velocity-dispersion closure at z≈0.07 would reveal whether that matters.
  • Editorial inference: the same five-statistic pipeline applied to future data could be extended to measure fσ8 differentially in redshift bins, turning the TF anomaly test into a systematic check on distance-calibration zero-points.

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 / 4 minor

Summary. The paper presents a measurement of the growth rate fσ8 from the DESI DR1 Peculiar Velocity survey, jointly analysing the momentum auto-correlation functions ψ1 and ψ2, the BGS galaxy clustering monopole and quadrupole, and the galaxy–momentum cross-correlation dipole. Nonlinear models are built from 1-loop Eulerian perturbation theory power spectra (taken from the companion paper Qin et al., in prep.) and are fit for five parameters [fσ8, b1σ8, b2σ8, σ²_vT, σ²_vS] over 24–120 h⁻¹Mpc using a covariance matrix from 675 AbacusSummit mocks. The fiducial full five-statistic fit gives fσ8 = 0.391^{+0.080}_{-0.081} at z_eff = 0.07 (Eq. 36); combining with the companion power-spectrum and maximum-likelihood analyses gives a consensus fσ8(z=0.07) = 0.4497 ± 0.0548, consistent with Planck+ΛCDM, and a joint fit with DESI full-shape clustering yields γ_L = 0.580 ± 0.110. The pipeline is validated on 300 mocks, recovering the fiducial mock fσ8, and the dependence on the fitting range is tested. The TF sample is restricted to z < 0.05 because of an unexplained excess correlation at higher redshift.

Significance. If the result holds, this is a valuable growth-rate measurement at z ≈ 0.07 from the largest peculiar-velocity sample to date, and the three-method consensus provides a competitive local-universe anchor for tests of gravity. The paper has genuine strengths: it releases a new public estimator code (crosscorr) with cross-validation against corrfunc, performs an extensive 300-mock validation showing unbiased recovery, tests stability to the fitting range (Fig. 7), is transparent about the TF-sample anomaly, and its results are mutually consistent across methods and with Planck+ΛCDM. However, the central nonlinear model is not described in this paper (companion in prep.), the mock validation is performed at z = 0.2 while the data are at z ≈ 0.07, and the quoted errors are purely statistical. These issues weaken the 'validated/unbiased' framing but do not, by themselves, invalidate the measurement.

major comments (3)
  1. [§2.3, §4.2 (Fig. 5)] The mock validation is performed on AbacusSummit snapshots at z = 0.2, while the data have z_eff = 0.07 and the quoted fσ8 is at z = 0.07. The paper itself notes that this is the lowest-redshift snapshot fit with an HOD model and defers a z ≈ 0.1 re-fit to future work. On the fitted scales (24–120 h⁻¹Mpc) the 1-loop EPT loop terms and the two velocity-dispersion parameters σ²_vT, σ²_vS absorb small-scale physics in a redshift-dependent way; nothing in the paper demonstrates that a model validated at z = 0.2 is unbiased at z = 0.07 at the claimed level. Please either validate at the z = 0.1 AbacusSummit snapshot (stated to be available) or provide an explicit quantitative argument that the redshift transfer is safe.
  2. [§3.1] The nonlinear density and momentum power-spectrum models are the core of the analysis, yet they are taken wholesale from Qin et al. (in prep.), and the text states 'We will not describe in detail how these power spectra models are produced.' The central unbiased-recovery claim therefore rests on an unpublished model that the reader cannot assess. The companion paper must be made available and referenced (at least as a preprint), with a summary of its construction and validation; alternatively, the essential ingredients—loop terms, bias expansion, and velocity-dispersion treatment—and their validation should be included here.
  3. [§2.2.2, Table 2, Eq. (36)] The z < 0.05 cut on the TF sample is data-driven: the excess correlation was identified from the data during the analysis and its cause is 'yet to be understood.' Moreover, the momentum-only fit to the z-cut TF sample has χ²_ν ≈ 3.0 (Table 2), indicating the model describes that sample poorly even after the cut. Since only statistical errors are quoted, the impact of this unexplained excess and of the data-driven cut is not propagated into the final uncertainty. I request a systematic-error treatment—for example, a systematic term reflecting the FP-only vs FP+TF(z<0.05) difference (Δfσ8 ≈ 0.05 in Table 2) or a marginalization over the TF cut choice—so that Eq. (36) reflects all identified uncertainties.
minor comments (4)
  1. [§2.2.2] Typo: 'contains 73,686 FP velocities and and 2,929 TF velocities' (duplicate 'and').
  2. [Table 2] The very poor χ²_ν = 2.992 for the TF(z<0.05) momentum-only fit, and the improvement in χ² when TF(z<0.05) is added to the FP+BGS five-statistic fit (1.518 → 1.215), are left unexplained in the text; a brief discussion would help the reader interpret the role of the TF sample.
  3. [§4.2, Fig. 7] A mild systematic trend of fσ8 with the lower fitting bound is acknowledged but not quantified; a sentence on its amplitude relative to the statistical error would clarify the robustness of the adopted 24–120 h⁻¹Mpc range.
  4. [§4.3.5] The consensus value and γ_L measurement rely on companion papers (Bautista et al., Qin et al., Lai et al., all in prep.); the text should state explicitly which results are preliminary pending those papers becoming available.

Circularity Check

0 steps flagged

Growth-rate measurement is a genuine likelihood fit to independent data; companion-paper model reliance is an external-validity caveat, not circularity.

full rationale

The central derivation chain is a standard parameter fit: the paper measures five correlation statistics from DESI DR1 data, constructs forward models from 1-loop Eulerian perturbation theory in which fσ8 is one of five free parameters (Section 3.1, Eqs. 6–17; Section 3.3, Eq. 34), and obtains fσ8 = 0.391^{+0.080}_{-0.081} from the fit (Eq. 36). The target quantity fσ8 is an output of the likelihood, not an input; no equation defines fσ8 in terms of the measured statistics or vice versa. The model is tested against 675 independent AbacusSummit N-body mocks with a known fiducial fσ8 = 0.462 (§2.3, §4.2), so the recovery of that fiducial is an external benchmark rather than a restatement of the fitted value. The consensus fσ8 = 0.4497 ± 0.0548 is a correlation-weighted combination of three separately implemented methods, and γ_L = 0.580 ± 0.110 is a derived constraint using that consensus, not a renamed input. The paper does rely on companion papers in prep. for the power-spectrum model (§3.1: 'We will not describe in detail how these power spectra models are produced... direct interested readers to the accompanying paper'), for catalogues, and for mocks; this is a completeness/external-support limitation, not circularity. Similarly, mock validation is at z = 0.2 while the data have z_eff = 0.07 (§2.3: 'this is different to the effective redshift of the DR1 dataset'), and the TF z<0.05 cut is motivated by an unexplained excess correlation (§2.2.2). These are isolated validity/correctness risks, not cases where a 'prediction' reduces by construction to a fitted parameter or to the authors' prior claims. No uniqueness theorem is imported, and no fitted nuisance parameter is renamed as a prediction.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central claim rests on five fitted parameters (fσ8, b1σ8, b2σ8, σ²_vT, σ²_vS) plus domain assumptions about the perturbation-theory model, bias model, Gaussianity of log-distance ratios, mock fidelity, and the ad hoc TF redshift cut. No new physical entities are introduced.

free parameters (5)
  • fσ8 = 0.391 (data), 0.484 (mock mean)
    The target parameter; fitted to the correlation-function data vector.
  • b1σ8 = 0.814 (data)
    Normalised linear galaxy bias, fitted jointly with fσ8.
  • b2σ8 = -0.252 (data)
    Normalised second-order local bias parameter, fitted jointly.
  • σ²_vT = 74.5 (h⁻¹ Mpc)² (data)
    Non-linear velocity dispersion for the loop terms P02, P04, P12, P22 and the vector part of P13.
  • σ²_vS = 161.1 (h⁻¹ Mpc)² (data)
    Non-linear velocity dispersion for loop term P03 and the scalar part of P13.
axioms (6)
  • domain assumption The 1-loop Eulerian perturbation theory power-spectrum model of Qin et al. (in prep.) is accurate for DESI BGS/PV tracers over 24–120 h⁻¹ Mpc.
    This model generates the entire template vector v_m(θ) (§3.1) but is not described or independently tested in this paper.
  • domain assumption The galaxy density field is adequately described by local linear and quadratic bias (b1, b2).
    The galaxy auto-correlation model (Eq. 15) uses Kaiser RSD with b1, and b2 is fitted as second-order bias; bias model is assumed adequate at these scales.
  • domain assumption The peculiar velocity field is irrotational, so the ψ1 and ψ2 momentum correlations contain all the velocity information.
    Invoked to justify the momentum auto-correlation model (§3.1.1, following Gorski 1988).
  • domain assumption Log-distance ratios η are Gaussian-distributed with zero mean in the likelihood.
    The likelihood analysis assumes multivariate Gaussian zero-mean η (§3.2.1, following Springob et al. 2014).
  • domain assumption The AbacusSummit mocks faithfully reproduce the DESI DR1 selection, clustering, and velocity noise, so their covariance matrix is applicable to the data.
    The mocks (§2.3) provide the covariance and validation; they are from a z=0.2 snapshot fitted with HOD, not z=0.07, as the paper acknowledges.
  • ad hoc to paper The TF z<0.05 cut is a valid conservative treatment of an unexplained excess correlation.
    The paper states the cause of the TF z>0.05 excess is 'yet to be understood' (§2.2.2, Figure 1); the cut is motivated by the observed anomaly rather than a physical model.

pith-pipeline@v1.3.0-alltime-deepseek · 24582 in / 10938 out tokens · 93407 ms · 2026-08-03T18:48:38.816865+00:00 · methodology

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read the original abstract

Joint analysis of the local peculiar velocity and galaxy density fields offers a promising route to testing cosmological models of gravity. We present a measurement of the normalised growth rate of structure, $f\sigma_8$, from the two-point correlations of velocity and density tracers from the DESI DR1 Peculiar Velocity and Bright Galaxy Surveys, the largest catalogues of their kind assembled to date. We fit the two-point correlation measurements with non-linear correlation function models, constructed from density and momentum power spectra generated using 1-loop Eulerian perturbation theory, and validate our methodology using representative mock catalogues. We find $f\sigma_8 = 0.391^{+0.080}_{-0.081}$, consistent to within $1\sigma$ with accompanying analyses of the same datasets using power spectrum and maximum-likelihood fields methods. Combining these growth rate results from different methods including appropriate correlations, we find a consensus determination $f\sigma_8(z = 0.07) = 0.4497 \pm 0.0548$, consistent with predictions from \textit{Planck}$+\Lambda$CDM cosmology. Jointly fitting to this consensus low-redshift growth rate and the DESI DR1 full-shape clustering dataset, we measure gravitational growth index $\gamma_{\rm L} = 0.580^{+0.110}_{-0.110}$, consistent with the prediction of general relativity.

Figures

Figures reproduced from arXiv: 2512.03230 by A. Carr, A. Cuceu, A. de la Macorra, A. Font-Ribera, A. G. Kim, A. J. Amsellem, A. Kremin, A. Leauthaud, A. Meisner, A. Mu\~noz-Guti\'errez, B. A. Weaver, C. Blake, C. Howlett, C. Lamman, C. Poppett, C. Ross, D. Bianchi, D. Brooks, D. Huterer, D. Kirkby, D. Schlegel, D. Sprayberry, E. Chaussidon, E. Gazta\~naga, E. Sanchez, F. Prada, F. Qin, G. Gutierrez, G. Rossi, G. Tarl\'e, H. K. Herrera-Alcantar, H. Zou, I. P\'erez-R\`afols, J. Aguilar, J. Bautista, J. E. Forero-Romero, J. Guy, J. Moustakas, J. Silber, K. Douglass, K. Honscheid, K. Said, L. Le Guillou, M. E. Levi, M. Ishak, M. Landriau, M. Manera, M. Schubnell, N. Palanque-Delabrouille, O. Lahav, P. Doel, P. Zarrouk, R. Joyce, R. J. Turner, R. Kehoe, R. Miquel, S. Ahlen, S. BenZvi, S. Ferraro, S. Gontcho A Gontcho, S. Nadathur, T. Claybaugh, W. J. Percival, Y. Lai.

Figure 1
Figure 1. Figure 1: The ψ1 correlation function for different velocity datasets tested in our analysis: the FP sample (black points), the TF sample (red points), the TF sample with a z < 0.05 cut (green points), and the combined sample (blue points). The solid line is the fiducial model. The original TF sample shows a high amplitude of correlation, leading us to apply a redshift cut z < 0.05 for the cosmological analysis. red… view at source ↗
Figure 2
Figure 2. Figure 2: A visualisation of the geometry of two galaxies A and B in relation to an observer O. Vectors separating the observer from galaxies A and B are described by ⃗ra and ⃗rb, respectively, while ⃗r is the vector separating A and B. The three-dimensional velocity of the galaxies are represented by ⃗va and ⃗vb, while the measurable line of sight component of the velocity is given by ua and ub. The cosines of the … view at source ↗
Figure 3
Figure 3. Figure 3: The correlation matrix used in this analysis, generated from all 675 mocks and using the fitting range 24 − 120 h−1 Mpc for each statistic. For a bin width of 6 h−1 Mpc this corresponds to 16 bins per statistic, and hence a matrix with dimensions 80 × 80. We employ a colour bar such that bins with higher correlation are redder, and bins that exhibit more anti-correlation are bluer. Bins on the diagonal are… view at source ↗
Figure 4
Figure 4. Figure 4: The five mock mean and data correlation functions that we consider in this analysis, and the best-fitting models for each. The light blue shaded region depicts the mock mean and 1σ errors as determined from all 675 mocks. The red points represents the measurements made from the DESI DR1 data, using BGS clustering data, FP velocity data, and the z-cut TF velocity data. The errors on these points are the sam… view at source ↗
Figure 5
Figure 5. Figure 5: The best-fitting values of fσ8 for 300 of the AbacusSummit clustering and velocity mocks, plotted against the error in those values obtained from an MCMC analysis. The mock data includes both FP and TF velocity samples, and all five correlation function statistics were used to fit for the model parameters within a fitting range 24 - 120 h−1 Mpc. The points are colour-coded by the minimum reduced χ 2 value,… view at source ↗
Figure 6
Figure 6. Figure 6: The joint confidence region for all parameters when fitting to the mock mean of the five correlation functions. Differently shaded regions in the 2D contours show the 1σ and 2σ confidence intervals, and the three dashed lines in the 1D posterior probabilities indicate the 16th, 50th, and 84th quantiles, representing the 68% confidence interval. these statistics. 4.3.3. Momentum and galaxy auto-correlation … view at source ↗
Figure 7
Figure 7. Figure 7: Measurements of fσ8 obtained from a χ 2 minimisation algorithm using the mock mean correlation functions, as a function of both the upper and lower bounds of the fitting range of separations. The upper bounds considered are [96, 102, 108, 112, 118, 124, 130, 136] h−1 Mpc. Lower bounds of 12 h−1 Mpc are shown in blue, 18 h−1 Mpc are shown in yellow, 24 h−1 Mpc are shown in green, and 30 h−1 Mpc are shown in… view at source ↗
Figure 8
Figure 8. Figure 8: Measurements of fσ8 using different combinations of input data, and fitting to different combinations of correlation statistics. From left to right, we fit using only the momentum correlations [ψ1 +ψ2], only the galaxy clustering correlations [ξ 0 gg +ξ 2 gg], the momentum and galaxy auto-correlations together [ψ1 +ψ2 + ξ 0 gg +ξ 2 gg], and finally all five statistics [ψ1 +ψ2 + ξ 0 gg +ξ 2 gg +ξ 1 gu]. Res… view at source ↗
Figure 9
Figure 9. Figure 9: The joint confidence regions for all parameters when fitting to the five correlation functions of the BGS + FP + TF z-cut samples for the DESI DR1 dataset. Differently shaded regions in the 2D contours show the 1σ and 2σ confidence intervals, and the three dashed lines in the 1D posterior probabilities indicate the 16th, 50th, and 84th quantiles, representing the 68% confidence interval. to be our fiducial… view at source ↗
Figure 10
Figure 10. Figure 10: Various measurements of fσ8, as a function of the effective redshifts of their respective datasets. Measurements may be slightly moved from their effective redshift for visual clarity. The three individual results from the DESI DR1 PV survey are shown in blue, and the combined consensus determination of fσ8 from these results is shown in black and marked by a star. Other results from the literature obtain… view at source ↗

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Forward citations

Cited by 8 Pith papers

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