{"id":"b917a4ba-658c-45bf-840f-98e20fd4e176","arxiv_id":"2607.19619","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"DESI DR2 Lyman-alpha BAO measurements split into three redshift bins trace the expansion rate H(z) over z≈2.1–2.8, yielding a power-law slope n=1.34±0.16 consistent with matter-dominated expansion.","lead":"A new DESI analysis splits the Lyman-alpha forest into three redshift ranges and measures baryon acoustic oscillation distances at three separate epochs in the early universe. The results trace how the expansion rate evolved over z≈2–3, consistent with standard matter-dominated expansion, and modestly improve curvature constraints.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Distortion matrix truncation at 300 h−1 Mpc, acknowledged as insufficient for the cross-correlation, could bias the redshift-dependent DH/rd trajectory and hence n=1.34±0.16.","rationale":"The reader identified the same load-bearing concern: the 300 h−1 Mpc line-of-sight extent of the distortion matrix is explicitly acknowledged in the paper as insufficient for the cross-correlation, which drives the DH/rd measurement. If this truncation biases the cross-correlation BAO peak in a redshift-dependent manner, the central expansion-history claim (n=1.34±0.16) would be compromised. The mock validation does not fully eliminate the concern because the mocks use the same truncated pipeline, so they test internal consistency but not the validity of the truncation itself. Other aspects of the paper are solid: the internal math is consistent, the robustness tests cover a wide range of modeling choices, the auto- and cross-correlations agree, and the cosmological constraints are internally consistent. Therefore the appropriate verdict remains CONDITIONAL, pending the concrete check of a larger distortion-matrix extent. My read does not change the reader's verdict; the concern is precisely the one flagged as weakest, and it warrants further testing before the central claim is taken at face value.","tokens_in":30192,"tokens_out":14110,"duration_ms":133296,"concrete_test":"Recompute the BAO fits using a distortion matrix with a line-of-sight extent of 400 h−1 Mpc (or 600 h−1 Mpc) on the same DESI DR2 data and on the 400 mocks, keeping all other analysis choices fixed. If the recovered α∥ in any redshift bin shifts by more than σ/3 relative to the baseline, then the DH/rd evolution and n are biased by the truncation; if shifts are negligible, the concern is resolved. An additional targeted test: generate a mock realization with a known power spectrum that includes significant BAO signal at pair separations >300 h−1 Mpc and analyze it with the 300 h−1 Mpc distortion matrix; any bias in α∥ would reveal the truncation effect.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—a direct measurement of the expansion-law index n=1.34±0.16 from three DH/rd values—rests on the radial BAO scale, which is primarily constrained by the Lyα×QSO cross-correlation. In §2.2, the distortion matrix that maps true to measured separations is computed with a line-of-sight extent of 300 h−1 Mpc. The paper's own footnote (page 4, footnote 1) states that this extent is sufficient for the auto-correlation 'but not for the cross-correlation, which would ideally require ~400 h−1 Mpc.' Because the Lyα forest spans roughly 500–600 h−1 Mpc in the line-of-sight direction (rest-frame 1040–1205 Å at z≈2.5), the projection operator η mixes pixels over this full range. A 300 h−1 Mpc truncation omits contributions from true separations beyond that scale when predicting the measured cross-correlation. If those omitted contributions distort the BAO peak in a redshift-dependent way (e.g., because the forest comoving length varies with z), the recovered α∥ shifts across bins, biasing the DH/rd trajectory and the derived n=1.34±0.16. The 400-mock validation is reassuring—stacked fits recover α=1 within σ/3—but the mocks are processed with the same truncated distortion matrix, so they cannot independently expose this specific modeling error. A dedicated test with a larger matrix extent is needed to confirm that the truncation is benign at the claimed precision.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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).","tokens_in":30601,"tokens_out":8935,"duration_ms":81657,"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":[{"comment":"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.","section":"§2.2, footnote 1"},{"comment":"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%.","section":"§3.2, Table 1"},{"comment":"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.","section":"§5.1, Table 2"}],"minor_comments":[{"comment":"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.","section":"§5.2 and Abstract"},{"comment":"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.","section":"Table 1"},{"comment":"The caption says the horizontal axis is log(1+z), but the axis is labeled z. Please make the figure and caption consistent.","section":"Figure 11"},{"comment":"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.","section":"§2.2, Eq. (2.6)"},{"comment":"There are several formatting artifacts (e.g., 'Vegapackage', 'T able', inconsistent χ2 spacing). A careful proofreading pass is recommended.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is transparent about its approximations, and I see no evidence of misrepresentation. The main technical obstacle is the untested 300 h−1Mpc distortion-matrix truncation for the cross-correlation; because the mocks share the same truncation, the existing validation cannot certify the central n measurement. The author overlap with the DESIDR2-Lyα validation paper is substantial, so the editor may wish to confirm that the calibration mocks are used appropriately. The paper is otherwise well within JCAP scope and, after the requested tests and a systematic-uncertainty discussion, would be a suitable contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read it. Short version: this is a genuine step — first multi-redshift Lyα BAO analysis with DESI, three bins at zeff = 2.13, 2.40, 2.81, per-bin ~1.1–1.2% isotropic precision, DH/rd decreasing from 9.40 to 7.22, and a slope n = 1.34 ± 0.16. What is actually new: pair-level binning, three-bin distances, the slope measurement, and self-consistent bias evolution (γα = 3.05, γβ = −0.97, γQ = 1.56). The validation is real: 400 mocks, pull distributions consistent with N(0,1), stacked fits within σ/3, and a broad set of robustness tests. I think the central BAO scales are solid.\n\nSoft spots, in order of importance. (1) The distortion matrix is truncated at 300 h−1 Mpc; the paper's own footnote says that is sufficient for the auto-correlation but not the cross-correlation, which would ideally need ~400. The cross-correlation is the main handle on the radial scale, so this could in principle shift the DH/rd trajectory and n. The mocks share the same truncation, so they cannot expose that bias. This does not make the paper wrong, but it is a specific modeling check I would want before quoting n = 1.34 ± 0.16 at face value. (2) The lowest bin has PTE = 0.01; the paper traces it to small-scale and line-of-sight residuals plus covariance smoothing. The robustness tests show the BAO scale is stable, and the mock χ2 shift explains part of it, but it remains a bit unsatisfying. (3) The γβ RSD-evolution result is explicitly flagged as lacking a full DLA-masking systematics assessment, so treat it as preliminary. (4) The cosmological constraints in §5.4 do not come with the full DESI validation suite; the paper says so. Fine for interpretation, but not the main product.\n\nI do not think the circularity concern lands. The distances are fits to measured correlations, not predictions of the model; the mocks test the pipeline against known truth. The citation pattern is normal for a DESI analysis paper.\n\nWho gets value: Lyα/BAO practitioners, people working on redshift-binned distance measurements, and anyone who wants the first direct handle on H(z) at 2 < z < 3. It deserves a serious referee. My recommendation: engage, send to review, and ask for the larger distortion-matrix test and the DLA-masking assessment before the slope becomes a headline number.","headline":"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.","tokens_in":31562,"tokens_out":1763,"would_cite":true,"duration_ms":16642,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["baryon acoustic oscillations","Lyman-alpha forest","expansion history","Einstein-de Sitter","matter-dominated era","DESI DR2","redshift binning","Alcock-Paczyński parameter"],"falsifier":"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.","tokens_in":30019,"feed_emoji":"📏","tokens_out":10170,"duration_ms":75623,"temperature":0.7,"pith_summary":"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.","feed_headline":"Expansion index n=1.34±0.16 measured at z≈2–3","feed_subtitle":"Lyman-α BAO traces H(z) across z≈2–3: first direct test of Einstein–de Sitter growth.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Lyman-α BAO pins expansion slope n=1.34±0.16 at z≈2–3","Direct test of EdS growth: H(z)∝(1+z)^1.34 at z~2–3","Three-redshift BAO reveals Hubble expansion index n=1.34±0.16","DESI Lyman-α BAO: expansion history slope n=1.34±0.16 from z=2 to 3","Multi-redshift BAO constrains cosmic expansion: n=1.34±0.16"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Lyman-α BAO pins expansion slope n=1.34±0.16 at z≈2–3","Direct test of EdS growth: H(z)∝(1+z)^1.34 at z~2–3","Three-redshift BAO reveals Hubble expansion index n=1.34±0.16","DESI Lyman-α BAO: expansion history slope n=1.34±0.16 from z=2 to 3","Multi-redshift BAO constrains cosmic expansion: n=1.34±0.16"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000292,"raw_usage":{"total_tokens":1706,"prompt_tokens":1077,"completion_tokens":629,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":821,"completion_tokens_details":{"reasoning_tokens":489}},"tokens_in":821,"tokens_out":629,"duration_ms":5299,"temperature":1.0,"reasoning_tokens":489,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T12:12:39.617595+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}