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A 3σ transverse BAO detection at z=1.725 from 2,754 SDSS quasars yields θ_BAO=1.928°±0.094°, translating to D_A/r_d=10.906±0.532.

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2026-08-04 09:21 UTC pith:5XZTUHRI

load-bearing objection Two versions of the central result; body's single-shell measurement is plausible but its significance ignores look-elsewhere from shell selection. the 4 major comments →

arxiv 2510.15650 v2 pith:5XZTUHRI submitted 2025-10-17 astro-ph.CO

High-redshift transverse BAO measurements with the SDSS quasar catalog

Felipe Avila , Armando Bernui , Miguel A. Sabogal , Rafael C. Nunes This is my paper
classification astro-ph.CO
keywords transverse BAOangular correlation functionSDSS quasarsangular diameter distancesound horizonlarge-scale structuredark energycosmology
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's body reports a single, statistically significant detection of the baryon acoustic oscillation (BAO) peak in the angular correlation function of SDSS quasars, using 2,754 quasars in the redshift shell 1.72≤z≤1.73 (z_eff=1.725). Fitting a polynomial plus Gaussian, it measures the transverse BAO angular scale θ_BAO=1.928°±0.094° (SNR=2.33; S_BAO=0.996, claimed as 3σ). Through D_A/r_d=1/[(1+z)θ_BAO], this becomes a scaled angular diameter distance D_A/r_d=10.906±0.532, a ~5% measurement that fills the gap between existing transverse BAO data at z=0.63 and z=2.225. The paper argues the thin shell (Δz=0.01) and high redshift make projection corrections negligible, so the measurement is nearly independent of the fiducial cosmology. It also finds, when combined with 16 literature θ_BAO points, flat-ΛCDM parameters Ω_m≈0.42 and h r_d≈98–99 Mpc, consistent with Planck and DESI. The abstract, however, describes two detections (θ_BAO=1.911°±0.062° and 1.727°±0.081° at z=1.725 and 1.775) with the same pipeline; the body's main result is the single measurement.

Core claim

The central claim is that the BAO feature appears in the quasar angular correlation function at z≈1.725, and its fitted angular position is the transverse BAO scale. Using the Landy–Szalay estimator on the SDSS DR16 quasar catalog in the shell 1.72≤z≤1.73, the paper obtains a correlation function whose best fit (Eq. 4) gives θ_BAO=1.928°±0.094° with the Gaussian amplitude posterior yielding S_BAO=0.996. The paper converts this to D_A/r_d=10.906±0.532, asserting that projection effects shift the peak by <1% because the shell is thin and the redshift high. It further claims this new point is consistent with Planck-ΛCDM and DESI when included in a 17-point θ_BAO compilation.

What carries the argument

The central object is the two-point angular correlation function (2PACF) ω(θ), computed with the Landy–Szalay estimator. The BAO signal is extracted by fitting ω(θ)=a+bθ+cθ²+C exp[−(θ−θ_BAO)²/(2σ²)], where C is the Gaussian amplitude and θ_BAO its centroid. Detection significance is quantified by S_BAO=∫P(C)dC, the posterior probability that C>0, with a claim when S_BAO>0.95. The covariance matrix for the fit is theoretical (Eq. 3), built from the fiducial Planck angular power spectrum plus shot noise, so the parameter errors are not shot-noise limited. The distance conversion uses the geometric relation D_A/r_d=1/[(1+z)θ_BAO] for a thin shell.

Load-bearing premise

The load-bearing premise is that the bump fitted at θ=1.928° in the 1.72–1.73 shell is the BAO peak and not a random fluctuation of the quasar correlation; the paper scans ~50 redshift shells and selects this one without calibrating how often a ≥2.3-SNR bump appears by chance in such a scan.

What would settle it

Run the identical pipeline on the same data with shuffled right ascensions (or on mock catalogs without BAO), generating null realizations of the correlation function in all 50 shells. If bumps with SNR≥2.3 appear as frequently in the nulls as in the data, the 3σ claim is not distinguishable from noise. Alternatively, re-fit the shell 1.72–1.73 with the position of the Gaussian fixed to the acoustic scale predicted from independent data; if the fit's likelihood is only marginally worse, but the amplitude C is consistent with zero, the peak is likely spurious.

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

If this is right

  • If the detection holds, cosmology gains a new model-nearly-independent distance measurement at z≈1.725 with ~5% precision, filling an empty stretch between z=0.63 and z=2.225 in transverse BAO data.
  • Combined with the existing 16-point θ_BAO compilation, the new point shifts the flat-ΛCDM best fit to Ω_m≈0.42, h r_d≈98–99 Mpc, in 1σ agreement with both Planck and DESI constraints.
  • This demonstrates that thin-shell quasar tomography can extract BAO in a regime (z~1.7) previously unreachable with angular correlation surveys.
  • If the two-detection version of the abstract is the final analysis, the method would provide distance anchors at two redshifts simultaneously, strengthening dark-energy dynamics tests.
  • The high-redshift anchor helps distinguish between models that fit low-z BAO but diverge at z>1, such as dynamical dark energy or early dark energy.

Where Pith is reading between the lines

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

  • The abstract and the body disagree on the number of detections and on the central values (two points vs one). This is an internal inconsistency in the manuscript itself; readers should verify which version reflects the final analysis before using the numbers. (This is the editor's note, not a claim of the paper.)
  • The measured θ_BAO≈1.928° sits about 12% above the Planck-ΛCDM prediction of ~1.72°. If the detection is real and not a noise fluctuation, this offset implies an angular diameter distance larger than ΛCDM predicts at z≈1.7, a potential hint for new physics or a higher sound horizon.
  • The significance estimate S_BAO comes from the same fit that locates the peak. A stronger test would be an end-to-end null simulation or a look-elsewhere correction across the ~50 shells scanned; the paper does not provide that, so the true false-alarm rate is not yet calibrated.
  • A direct extension: apply the same pipeline to neighboring shells (e.g., 1.74–1.76) with larger quasar samples, to see whether the offset and detection significance follow the expected BAO trend or behave like random fluctuations.

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

4 major / 5 minor

Summary. The paper analyzes the SDSS-DR16 quasar catalog to search for transverse BAO in thin redshift shells between z=1.5 and z=2.0. The body of the paper reports a single detection in the shell 1.72≤z≤1.73 (2,754 quasars) with θ_BAO=1.928°±0.094° and a corresponding angular diameter distance D_A/r_d=10.906±0.532 at z_eff=1.725, claimed as a 3σ detection. This measurement is then combined with 16 literature points to constrain flat-ΛCDM parameters, yielding Ω_m=0.421^{+0.073}_{-0.10} and h r_d=98.1^{+2.9}_{-2.6}. The arXiv abstract, however, describes a different analysis with two detections (θ_BAO=1.911°±0.062° and 1.727°±0.081°), different significances, and different cosmological parameters. The body's single-shell result is internally consistent, but the paper as submitted contains a major internal inconsistency between the abstract and the main text, and the claimed detection significance lacks a trials correction for the multi-shell search.

Significance. If the detected peak is genuinely the BAO scale, the measurement would provide a valuable new transverse BAO datum at z≈1.7, partially filling the gap between z≈0.63 and z≈2.2. The paper's use of a narrow redshift shell to reduce projection effects, a public catalog, and a full analytical covariance matrix are strengths, and the derivation from θ_BAO to D_A/r_d via Eq. (8) is straightforward and correctly reproduced. However, the significance of the detection and the consistency of the reported numbers are not yet established, so the scientific value of the claimed result cannot be assessed until these issues are resolved.

major comments (4)
  1. [Abstract vs. §III-A, Eqs. (7)–(9)] The abstract and the body report incompatible central results. The abstract claims two detections: θ_BAO=1.911°±0.062° (3.4σ) at z_eff=1.725 and θ_BAO=1.727°±0.081° (3.0σ) at z_eff=1.775, leading to D_A/r_d=11.00±0.36 and 11.96±0.56, with Ω_m=0.41±0.06 and h r_d=99.3±2.0. The body reports a single detection, θ_BAO=1.928°±0.094° and D_A/r_d=10.906±0.532 (Eq. 9), and Table I gives Ω_m=0.421^{+0.073}_{-0.10}, h r_d=98.1^{+2.9}_{-2.6}. These cannot both be the result of the same analysis. The manuscript must state which analysis is the actual one and align the abstract, body, tables, and figures accordingly.
  2. [§III-A, shell selection and Eqs. (4)–(5)] The claimed 3σ detection (S_BAO=0.996) is computed from the posterior of the Gaussian amplitude C in the single shell z∈[1.72,1.73]. This shell was selected after a scan of ~50 thin shells over 1.5<z<2.0, as stated in the abstract and implied by 'After analyses, we found a BAO signal...' in Sec. III. No trials correction or mock-based false-alarm rate is provided. A scan of 50 shells will produce a maximum bump with an SNR larger than the per-shell threshold even in the absence of a true BAO. The quoted significance is therefore a local, not a global, quantity, and it does not support the detection claim without calibration. This is load-bearing: if the bump is a noise fluctuation, θ_BAO is not the BAO scale and Eq. (9) does not measure a distance. Please provide a global p-value, e.g., from mock catalogs or from the distribution of the maximum S_BAO over all 50 shells.
  3. [§III-A, Eq. (4) and detection definition] The detection probability S_BAO=∫P(C)dC quantifies the posterior probability that the Gaussian amplitude C is positive. It does not test whether the fitted Gaussian is the BAO peak rather than a random feature of the broadband angular correlation. Since the Gaussian center θ_BAO, width σ, and amplitude C are all free, the model can absorb a noise peak. A robustness test against a no-Gaussian model or against a fixed BAO template is needed to demonstrate that the bump at θ=1.928° is actually the acoustic feature and not a continuum fluctuation. This concern is closely related to the trials issue and should be addressed together.
  4. [§III-B, Table I] The cosmological fit in Table I is based on 17 measurements: 14 from Menote & Marra (2022), one from de Carvalho et al. (2018), one from de Carvalho et al. (2021), plus the one from this work. This is internally consistent with the body. However, the abstract's fit uses two new measurements, which would imply an 18-point compilation and different best-fit parameters. The discrepancy between the abstract's Ω_m=0.41±0.06, h r_d=99.3±2.0 and the body's Ω_m=0.421^{+0.073}_{-0.10}, h r_d=98.1^{+2.9}_{-2.6} is not merely a rounding issue; the central values and error bars differ. Please reconcile these numbers.
minor comments (5)
  1. [§III-A, Eq. (8)] Equation (8) uses θ_BAO, but the text reports θ_BAO in degrees. Please state explicitly that the conversion to D_A/r_d requires θ_BAO in radians, or show the conversion factor.
  2. [Fig. 1 and §II-B] Figure 1 shows error bars labeled as shot noise, while Fig. 2 emphasizes the difference between the theoretical covariance and shot noise. The text later uses the theoretical covariance for the fit. Please clarify which error bars are plotted in Fig. 1 and why the shot-noise errors are shown when the covariance model is used in the analysis.
  3. [References] Reference [54] is a placeholder (arXiv:XXXX.XXXXX). This must be completed before publication.
  4. [Title and formatting] The title contains a typo: 'atzeff' should be 'at z_eff'. Also, there are LaTeX/math formatting issues in the abstract and header.
  5. [§III-B, statistical significance] The statement that S_BAO=0.996 corresponds to '3σ' is not exact for a Gaussian distribution (3σ would be 0.9973). Please state the conversion convention used.

Circularity Check

1 steps flagged

Detection significance is computed from the same fitted Gaussian amplitude that defines the peak, with no trials correction for the shell scan; the central θ_BAO fit itself is not circular.

specific steps
  1. fitted input called prediction [Section III / Section III.A, Eqs. (4)-(5) and S_BAO result]
    "Since the parameter C governs the amplitude of the BAO peak, it can be used to quantify the confidence of its detection. The signal strength is defined as S_BAO ≡ ∫ P(C)dC ... From the posterior distribution of the parameter C, we obtain S_BAO = 0.996, corresponding to a 3σ detection, thereby confirming the presence of the BAO signal in our subsample."

    The 3σ is derived from the posterior of C, which is a free amplitude parameter of the same Gaussian in Eq. (4) whose center θ_BAO and width σ are also free parameters; the redshift shell was itself chosen after a scan ('After analyses, we found a BAO signal in the interval 1.72≤z≤1.73'). The detection significance therefore reports the fitted Gaussian's own amplitude rather than testing a pre-specified BAO feature, and no trials or false-alarm correction for the 50-shell scan is given. The result does not make θ_BAO equal to a model input, but the '3σ' claim is statistically forced by the fitting procedure rather than an independent confirmation.

full rationale

The central measurement θ_BAO = 1.928° ± 0.094° and the derived D_A/r_d = 10.906 ± 0.532 come from a direct Landy-Szalay estimate of the public SDSS eBOSS DR16 quasar catalog and a fit of the empirical model (4); they are not constructed from the Planck/DESI parameters used for later comparison, so the main distance claim is not circular. The detected amplitude significance, however, is computed from the same fitted Gaussian amplitude (Eq. 5), and the shell was selected after an unshown tomographic scan, so the quoted 3σ has a self-referential component that is not protected by a trials correction. This affects the detection claim but not the internal derivation of θ_BAO from the correlation function. The abstract/body numerical inconsistency is a reproducibility concern, not a circularity.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 0 invented entities

The central claim rests on: the empirical Gaussian+polynomial model for ω(θ); the analytic covariance computed from a Planck flat-ΛCDM spectrum; the assertion that Δz=0.01 at z≈1.7 suppresses projection smearing to <1%; and the assumption that the bump found in the selected shell is the BAO signal without a trials correction. No new physical entities are introduced. The abstract-only version additionally invokes a free parameter α that is not described in the body.

free parameters (6)
  • a, b, c — polynomial coefficients = not quoted
    Broadband model of ω(θ) in Eq. (4); fitted to the quasar-shell data; absorb low-order angular clustering.
  • C — Gaussian amplitude = not quoted (posterior used for S_BAO)
    Amplitude of the BAO bump; free in Eq. (4); the detection significance S_BAO=∫P(C)dC (Eq. 5) is computed from its posterior.
  • σ — Gaussian width = ≈0.2–0.4° (from Fig. 3)
    Width of the BAO bump, free in Eq. (4).
  • θ_BAO — Gaussian center = 1.928°±0.094° (body); 1.911°±0.062° and 1.727°±0.081° (abstract)
    The central measured quantity; its position is a free fit parameter, not a predicted value.
  • α — dimensionless shift parameter (abstract version only) = not given
    Invoked in the abstract's empirical parameterization to obtain the scaled distances; no equations or values appear in the manuscript body, which states the α parameter is not required.
  • Ω_m, h r_d (cosmological fit) = body: 0.421(+0.073/−0.10), 98.1(+2.9/−2.6) Mpc; abstract: 0.41±0.06, 99.3±2.0 Mpc
    Fitted to the 17/18-point θ_BAO compilation under flat ΛCDM (Table I, Fig. 5).
axioms (7)
  • standard math Landy-Szalay estimator is unbiased with minimal variance
    Eq. (1), §II A: the pair-count estimator is adopted on the basis of its standard statistical properties.
  • domain assumption Analytic covariance model with Planck Cℓ and shot noise 1/n̄ is accurate for thin-shell 2PACF in the linear regime
    Eq. (3), §II B: the full covariance is computed from a Planck flat-ΛCDM fiducial spectrum via CCL; deviations of the true cosmology change the quoted errors and S_BAO.
  • domain assumption Projection effects are <1% for Δz=0.01 at z≈1.7, so θ_FIT ≃ θ_BAO
    §II C and §III B: relies on Sánchez et al. 2011 [11]; if the correction were larger, the reported θ_BAO would be biased.
  • ad hoc to paper The empirical model ω(θ)=a+bθ+cθ²+C·Gaussian(θ_BAO,σ) adequately describes the angular correlation
    Eq. (4): adopted after the power-law model failed; the free polynomial and free Gaussian position/width increase the flexibility of the fit.
  • domain assumption Quasars trace matter with a linear bias on BAO scales
    §II: the 2PACF analysis and its interpretation assume quasar clustering follows linear structure formation on the relevant scales.
  • domain assumption Flatness Ω_k=0 for the cosmological interpretation
    §III B and Table I caption: the ΛCDM fits and the comparison to Planck/DESI assume a flat universe.
  • domain assumption The 17 (or 18) θ_BAO measurements are statistically independent
    §III B: the fit to the BAO compilation treats the literature measurements as independent points; no correlation matrix is modeled.

pith-pipeline@v1.3.0-alltime-deepseek · 10325 in / 26596 out tokens · 204841 ms · 2026-08-04T09:21:30.314131+00:00 · methodology

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read the original abstract

Transverse Baryon Acoustic Oscillation (BAO) measurements offer a robust geometric probe of the Universe expansion, presenting minimal dependence on fiducial cosmological models. In this work, we analyze the SDSS-DR16 quasar catalog to search for the 2D BAO signal in the unexplored redshift interval $1.5 \leq z \leq 2.0$. Performing a fine tomographic analysis in 50 thin disjoint redshift shells ($\Delta z = 0.01$), to suppress line-of-sight projection smearing, and incorporating a full analytical covariance matrix, we detect the acoustic peak in two uncorrelated redshift shells: $\theta_{\rm BAO} = 1.911^{\circ} \pm 0.062^{\circ}$ and $\theta_{\rm BAO} = 1.727^{\circ} \pm 0.081^{\circ}$ centered at $z_{\rm eff} = 1.725$ and $z_{\rm eff} = 1.775$, with statistical significances of $3.4\,\sigma$ and $3.0\,\sigma$, respectively. By introducing a dimensionless shift parameter $\alpha$ in our empirical parameterization procedure, we then obtain two scaled angular diameter distances: $D_A/r_d = 11.00 \pm 0.36$ at $z_{\rm eff}=1.725$ and $D_A/r_d = 11.96 \pm 0.56$ at $z_{\rm eff}=1.775$. Incorporating these two novel data points into a literature compilation of 16 transverse BAO measurements, we perform a flat-$\Lambda$CDM parameter estimation, obtaining $\Omega_{m,0} = 0.41 \pm 0.06$ and $h r_d = 99.3 \pm 2.0$ Mpc. Our measurements successfully bridge a significant observational gap at high redshift, which remain highly consistent with the constraints reported by the Planck and DESI collaborations, demonstrating the potential of quasar tomographic surveys for dynamical dark energy studies.

Figures

Figures reproduced from arXiv: 2510.15650 by Armando Bernui, Felipe Avila, Miguel A. Sabogal, Rafael C. Nunes.

Figure 1
Figure 1. Figure 1: FIG. 1. 2-point angular correlation function for the quasar [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The difference between the error from the theoretical [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Marginalized posterior distributions of the parameters of equation (4), obtained through the MCMC analysis of the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Best-fit of equation (4). The error bars were ob [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Statistical best-fit analysis for studying the consis [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

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