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REVIEW 3 major objections 5 minor 65 references

By splitting the Lyman-α forest into three redshift bins, this paper measures the expansion history over 2≲z≲3 directly, finding H(z)∝(1+z)^n with n=1.34±0.16.

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2026-08-01 12:12 UTC pith:F4LKI3C4

load-bearing objection First multi-redshift Lyα BAO from DESI: real distances and a 12% slope measurement, but the acknowledged distortion-matrix truncation for the cross-correlation needs testing before the headline n is quoted. the 3 major comments →

arxiv 2607.19619 v2 pith:F4LKI3C4 submitted 2026-07-21 astro-ph.CO

Probing the matter-dominated expansion with multi-redshift Lyman-α BAO from DESI DR2

Hiram K. Herrera-Alcantar , Julien Guy , Alma X. Gonzalez-Morales , Eric Armengaud , Edwin L. P\'erez-Ochoa , Cristhian Garcia-Quintero , J. Aguilar , S. Ahlen
show 55 more authors
F. Beutler D. Bianchi A. Brodzeller D. Brooks E. Chaussidon T. Claybaugh A. Cuceu K. S. Dawson A. de la Macorra Arjun Dey S. Ferraro A. Font-Ribera J. E. Forero-Romero E. Gazta\~naga G. Gutierrez C. Hahn K. Honscheid D. Huterer M. Ishak T. Karim R. Kehoe D. Kirkby A. Kremin O. Lahav A. Lambert M. Landriau L. Le Guillou M. Manera P. Martini A. Meisner R. Miquel J. Moustakas A. Mu\~noz-Guti\'errez S. Nadathur G. Niz E. Paillas N. Palanque-Delabrouille W. J. Percival C. Poppett F. Prada I. P\'erez-R\`afols C. Ravoux G. Rossi R. Ruggeri L. Samushia E. Sanchez C. Saulder D. Schlegel M. Schubnell H. Seo J. Silber G. Tarl\'e B. A. Weaver C. Y\`eche R. Zhou
This is my paper
classification astro-ph.CO
keywords baryon acoustic oscillationsLyman-alpha forestexpansion historyEinstein-de Sittermatter-dominated eraDESI DR2redshift binningAlcock-Paczyński parameter
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 splits the Lyman-α forest from the survey's second data release into three redshift bins, at effective redshifts 2.13, 2.40, and 2.81, and measures the baryon acoustic oscillation scale in each. Because the radial BAO scale is directly proportional to 1/H(z), the three bins trace the expansion rate through the matter-dominated era: the Hubble distance DH/rd falls from 9.40±0.20 to 7.22±0.17 across the bins. Fitting H(z)∝(1+z)^n gives n=1.34±0.16, consistent at 1σ with the Einstein–de Sitter value n=3/2 and with ΛCDM. The paper claims this is the first direct, cosmology-independent test of the matter-dominated expansion law in this redshift range, and the same fit also constrains the redshift evolution of Lyman-α forest and quasar clustering parameters.

Core claim

The central claim is that multi-redshift Lyman-α BAO analysis delivers a direct measurement of the expansion history at 2≲z≲3. Working from the same data products and model as the single-effective-redshift analysis, the authors assign each pixel–pixel or pixel–quasar pair to a redshift bin by its mean pair redshift, fit the BAO peaks in each bin, and validate the pipeline on 400 synthetic datasets. They recover unbiased BAO scales at ~1.1–1.2% isotropic precision per bin, and the radial distance DH/rd declines monotonically from 9.40±0.20 to 7.22±0.17. A power-law fit to these points yields H(z)∝(1+z)^n with n=1.34±0.16, a ~12%-precision constraint on the logarithmic slope of the expansion r

What carries the argument

The load-bearing object is pair-level redshift binning: each pair entering the correlation functions is assigned to one of three redshift bins according to its mean pair redshift, so a single Lyman-α forest can contribute to multiple bins. To handle the continuum-fitting distortions that this introduces, the distortion matrix is recomputed with the same pair-based restriction, and the metal-contamination matrices are updated accordingly. Per bin, the fit returns the BAO scale parameters α∥ and α⊥, which set DH/rd and DM/rd relative to a fiducial cosmology; the expansion-law index n then comes from a power-law fit to DH/rd at the three effective redshifts.

Load-bearing premise

The cross-correlation distortion matrix is truncated at a line-of-sight extent of 300 h⁻¹Mpc, which the paper itself notes is too short for the cross-correlation (about 400 h⁻¹Mpc would be needed); since the validation mocks use the same truncation, they cannot expose any resulting bias in DH/rd, on which the n=1.34±0.16 result depends.

What would settle it

Re-run the three-bin fits with a cross-correlation distortion matrix extended to at least 400 h⁻¹Mpc and check whether DH/rd at any bin (and hence the fitted n) shifts by more than about σ/3; alternatively, compare the n=1.34±0.16 result against a full-shape Lyman-α analysis or cosmic-chronometer H(z) measurements at z≈2–3, both of which are independent of the BAO-peak assumption.

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

If this is right

  • The three radial distance measurements are unbiased at the ~1% level and mutually consistent, so the expansion-history test is not an artifact of one redshift bin.
  • The value n=1.34±0.16 is the first direct high-redshift constraint on the expansion-law index over 2≲z≲3, probing the matter-dominated epoch.
  • The same three-bin fit yields self-consistent evolution of astrophysical clustering parameters, offering a simultaneous probe of cosmology and of the intergalactic medium.
  • Combining the three bins with galaxy and quasar BAO improves curvature constraints by ~12% in non-flat ΛCDM, with no significant changes for flat ΛCDM or w0waCDM.
  • Cross-bin correlations are consistent with zero, so the redshift-split measurements can be treated as independent and merged with other tracers.

Where Pith is reading between the lines

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

  • If the measured slope survives a larger distortion-matrix extent and independent cross-checks, it provides a direct observational handle on models that modify the expansion rate at z≈2–3—early dark energy, decaying dark matter, or non-standard recombination—where the n=3/2 law serves as the baseline.
  • The same pair-based binning could be extended to higher redshifts using Lyman-break galaxy forests or to future surveys with larger sky coverage, potentially tightening n from 12% precision toward the few-percent level.
  • The monotonic rise of the Alcock–Paczyński parameter DM/DH across the bins could be combined with the radial BAO measurement to break degeneracies between distance and clustering evolution, a test not performed here.
  • A dedicated study of DLA masking and of the HCD model is already flagged as needed; if the measured RSD evolution γ_β survives, it may become an astrophysical diagnostic of the thermal state of the intergalactic medium.

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. This paper presents a multi-redshift baryon acoustic oscillation (BAO) analysis of the DESI DR2 Lyman-α forest, splitting the Lyα auto-correlation and its cross-correlation with quasars into three pair-redshift bins with effective redshifts zeff = 2.13, 2.40, and 2.81. The authors measure the radial and transverse BAO scale parameters α∥ and α⊥ in each bin, convert them to DH/rd and DM/rd, and interpret the redshift evolution of DH/rd as a direct probe of the expansion history during the matter-dominated era, fitting H(z) ∝ (1+z)^n and obtaining n = 1.34 ± 0.16. They also measure the redshift evolution of the Lyα bias, RSD parameter, and quasar bias, and combine the three-bin distances with other DESI DR2 BAO tracers and external CMB/supernova data to derive cosmological constraints, reporting improved curvature precision relative to the single-bin Lyα analysis. The analysis pipeline is validated on 400 synthetic datasets (CoLoRe-QL and Saclay), with stacked fits within σ/3 and pull distributions consistent with N(0,1).

Significance. If the results hold, this is a valuable step forward: it is the first multi-redshift Lyα BAO measurement from DESI DR2, and the inferred slope n = 1.34 ± 0.16 would constitute the first direct measurement of the expansion-law index at 2 ≲ z ≲ 3, a regime where cosmic chronometers are scarce and where the matter-dominated scaling predicted by Friedmann equations can be tested. The paper is methodologically careful: it uses public codes (picca, vega), validates on 400 mocks with well-calibrated pulls, performs a broad robustness suite, and transparently reports limitations (the distortion-matrix extent, the low PTE in one bin, the exclusion of region B, DLA-masking caveats). The clustering-evolution measurements are self-consistent and agree with independent quasar clustering results, which strengthens the credibility of the analysis. However, the central expansion-history claim rests on an acknowledged but untested modeling approximation—the 300 h−1Mpc distortion-matrix truncation—and the quoted distance uncertainties appear to be statistical only. These issues must be addressed before the result can be taken at face value.

major comments (3)
  1. [§2.2, footnote 1] The distortion matrix is computed with a line-of-sight extent of 300 h−1Mpc, and the footnote states that this is sufficient for the auto-correlation but not for the cross-correlation, which would ideally require ~400 h−1Mpc. The cross-correlation contributes significant weight to the radial (α∥) constraint, and therefore to the DH/rd values in Table 2 and to the power-law slope n=1.34±0.16 in §5.2. Because the mock realizations are generated and analyzed with the same truncated matrix, the 400-mock validation cannot detect a bias from this truncation. I request a dedicated test with a larger (≥400 h−1Mpc) distortion matrix—on the mocks and, if feasible, on the data—or a quantitative estimate of the induced shift in α∥ per redshift bin. Without such a test, the central expansion-history claim rests on an acknowledged, untested approximation.
  2. [§3.2, Table 1] The baseline fit in the lowest-redshift bin has PTE=0.01 (Table 1). The paper attributes this to small-scale and line-of-sight residuals and to covariance-matrix smoothing, and shows that the BAO shifts under robustness variations are within σ/3. However, this bin anchors the low-redshift end of the DH/rd trajectory and therefore has direct leverage on n. The post-hoc PTE corrections bring the bin only to PTE≈0.08 (Section 3.2). Please either adopt a baseline whose PTE is acceptable (e.g., the r∈[60,160] h−1Mpc or reduced-µ configuration) and verify that the DH/rd trajectory and n are unchanged, or provide a quantitative upper bound on the bias in α∥ that the residual structure could induce. The present discussion is plausible but does not fully close the issue for a bin that formally rejects the model at 99%.
  3. [§5.1, Table 2] The distance measurements in Table 2 are quoted without a systematic error term, even though the DESI DR2 Lyα baseline analysis on which this paper builds adds a dedicated systematic uncertainty (e.g., DH/rd ≈0.026 systematic at zeff=2.33). The present analysis uses a truncated distortion matrix, region-A-only correlations, and a baseline with a low-PTE bin; all of these are acknowledged modeling approximations. If the reported error bars are statistical only, the uncertainty on n=1.34±0.16 is likely underestimated. Please either propagate a systematic term into DH/rd and n, or explicitly justify—with the σ/3 tests and the larger-matrix test requested above—that all identified modeling uncertainties are already covered.
minor comments (5)
  1. [§5.2 and Abstract] The phrase 'cosmology-independent test' overstates the case: the DH/rd values in Table 2 are obtained by multiplying the fitted α∥ by the fiducial cosmology's DH/rd at each effective redshift. What is actually measured is the deviation from that fiducial trajectory, which is standard BAO methodology, but the language should be qualified to avoid implying full independence of the fiducial choice.
  2. [Table 1] The degrees of freedom are listed as '4653−17'; please state the actual DoF value (4636) explicitly in the table for clarity, since this number is used in Figures 9 and 10.
  3. [Figure 11] The caption says the horizontal axis is log(1+z), but the axis is labeled z. Please make the figure and caption consistent.
  4. [§2.2, Eq. (2.6)] The notation z_k, z_p, and z_ref in Eq. (2.6) is not fully defined in the immediate text; a brief definition would improve readability.
  5. [General] There are several formatting artifacts (e.g., 'Vegapackage', 'T able', inconsistent χ2 spacing). A careful proofreading pass is recommended.

Circularity Check

0 steps flagged

No significant circularity: the multi-redshift BAO distances and n=1.34±0.16 are fits to measured correlation functions, not predictions forced by the model or by self-citation.

full rationale

The paper's central quantities—DH/rd in three redshift bins and the derived slope n=1.34±0.16—are obtained by fitting BAO scale parameters α∥ and α⊥ to the measured Lyα auto- and cross-correlation functions. These fits are calibrated to a fiducial cosmology only through the definitions α∥ = [DH/rd]/[DH/rd]_fid and α⊥ = [DM/rd]/[DM/rd]_fid (Eq. 3.1), which is standard practice and does not make the measurement equal to the input by construction; the α values are free parameters and can deviate from unity. The power-law slope n is explicitly a fit to the three measured DH/rd points, not a prediction derived from the model, and the paper compares it to both the EdS expectation (1.5) and a synthetic ΛCDM realization (1.42±0.16). The analysis leans heavily on DESIDR2-Lyα data products and modeling framework, and many citations are to the authors' own work, but the pipeline is validated against 400 synthetic datasets with known input truth (α∥=α⊥=1), and the quasar bias evolution is cross-checked against independent DESI clustering measurements. The acknowledged distortion-matrix truncation at 300 h−1 Mpc, stated in footnote 1 as insufficient for the cross-correlation ('would ideally require ~400 h−1 Mpc'), is a potential modeling systematic that could bias the DH/rd trajectory; it is not, however, a circular reduction of a prediction to an input. No load-bearing argument reduces a claimed prediction to a fitted parameter or to a self-citation chain. Therefore the paper exhibits no significant circularity, with only mild self-reliance that is not load-bearing.

Axiom & Free-Parameter Ledger

10 free parameters · 6 axioms · 0 invented entities

The measurement rests on the standard Lyα forest BAO modeling framework inherited from DESIDR2-Lyα: a linear-bias, RSD, metal-contamination, HCD, and quasar-redshift-error model with 15 fitted nuisance parameters per bin. No new physical entities are introduced; the main hand-chosen inputs are the redshift-bin boundaries and the fixed fiducial Planck 2018 cosmology.

free parameters (10)
  • Lyα bias bα (per bin) = -0.0703, -0.1428, -0.2286 (Table B.1)
    Fitted to the binned auto- and cross-correlation functions; marginalized in BAO fits.
  • RSD parameter βα (per bin) = 2.25, 1.469, 1.208 (Table B.1)
    Fitted; correlated with bα and HCD parameters.
  • Quasar bias bQ (per bin) = 3.206, 3.731, 4.35 (Table B.1)
    Fitted with uniform prior to allow redshift evolution.
  • Quasar redshift error σz and shift Δr∥ = σz≈2.3–3.4 h⁻¹Mpc; Δr∥≈0.39–1.06 h⁻¹Mpc
    Fitted to the cross-correlation; absorb quasar redshift systematics.
  • Proximity effect amplitude ξTP0 = 0.310, 0.489, 0.86
    Fitted; degenerate with fixed mean free path λUV=300 h⁻¹Mpc.
  • HCD parameters bHCD, βHCD, LHCD = bHCD≈-0.061 to -0.010; βHCD≈0.5; LHCD≈5 h⁻¹Mpc
    Fitted with priors; b′α,β′α defined to break degeneracy.
  • Metal biases and noise amplitude (bSiII/bSiIII/bCIV, anoise) = see Table B.1
    Fitted nuisance parameters for metal contamination and correlated noise.
  • Power-law slopes γα, γβ, γQ, n = 3.05±0.16, -0.97±0.26, 1.56±0.23, 1.34±0.16
    Fitted to the binned derived parameters; γβ carries the DLA-masking caveat.
  • Redshift bin boundaries = zpair≤2.25, 2.25–2.6, >2.6
    Hand-chosen for comparable statistical power; not optimized.
  • BAO broadening and small-scale correction = fixed per bin from LPT/ACCEL2
    Set by simulation predictions, not fit.
axioms (6)
  • standard math Friedmann equations; in matter domination H(z)∝(1+z)^{3/2}
    Background for the Einstein-de Sitter test in §5.2.
  • domain assumption Lyα forest flux contrast traces matter density with linear bias and RSD; HCD/DLA effects modeled separately
    Standard large-scale-structure modeling assumed throughout the fit (§3.1).
  • domain assumption The continuum-fitting projection operator η correctly maps the measured field to the true projected field
    Distortion-matrix treatment in §2.2; assumed uncorrelated continuum errors per forest.
  • domain assumption Metal contamination described by known SiII/SiIII/CIV transitions with redshift-independent relative strengths
    Metal-matrix model in §2.3.
  • domain assumption Fiducial flat ΛCDM Planck 2018 cosmology used to convert α∥,α⊥ to physical distances and effective redshifts
    §3.1; standard BAO practice; results weakly dependent on fiducial.
  • ad hoc to paper Cross-bin covariances negligible except within-bin α∥–α⊥ correlations
    Appendix A: MC and mock scatter show |ρ|≲0.02–0.06; set to zero in cosmology fits.

pith-pipeline@v1.3.0-alltime-deepseek · 30118 in / 16919 out tokens · 162389 ms · 2026-08-01T12:12:39.617595+00:00 · methodology

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read the original abstract

We present a multi-redshift Baryon Acoustic Oscillations (BAO) analysis of the DESI Data Release 2 (DR2) Lyman-$\alpha$ (Ly$\alpha$) forest, splitting the forest auto-correlation and its cross-correlation with quasars into three redshift bins. We obtain BAO measurements at effective redshifts $z_{\rm eff} = 2.13$, $2.40$, and $2.81$ with $\sim2.0$--$2.5\%$ precision per bin in the radial and transverse directions, corresponding to $\sim1.1$--$1.2\%$ precision for the isotropic BAO measurement. Using the same data products and modeling framework as the DESI DR2 Ly$\alpha$ BAO analysis, we validate the pipeline on $400$ synthetic datasets and find unbiased BAO recovery with well-calibrated uncertainties. The measurements show an increase in the isotropic dilation parameter $D_V/r_d$ from $30.26\pm0.39$ to $32.22\pm0.47$ and in the Alcock-Paczy\'nski parameter $D_M/D_H$ from $3.96\pm0.15$ to $5.63^{+0.22}_{-0.24}$. The Hubble distance $D_H/r_d$ decreases from $9.40\pm0.20$ to $7.22\pm0.17$, providing a direct measurement of the expansion history consistent with $\Lambda$CDM and the expected matter-dominated scaling, with $H(z)\propto(1+z)^n$ giving $n=1.34\pm0.16$. The redshift split also provides a self-consistent measurement of clustering evolution: the Ly$\alpha$ forest bias evolves as $(1+z)^\gamma$ with $\gamma_\alpha=3.05\pm0.16$, the RSD parameter has a redshift evolution described by $\gamma_\beta=-0.97\pm0.26$, and the quasar bias evolves with $\gamma_Q=1.56\pm0.23$, consistent with independent quasar clustering measurements. Combining these three-bin BAO measurements with DESI DR2 galaxy and quasar BAO measurements yields cosmological constraints consistent with the single-bin Ly$\alpha$ BAO analysis in flat $\Lambda$CDM and $w_0w_a$CDM and improves curvature constraints by $\sim12\%$ in $\Lambda$CDM$+\Omega_\mathrm{K}$.

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Reference graph

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