REVIEW
A blind spot in transverse BAO calibration
Cosmology and Nongalactic Astrophysics · Submitted 20 Aug 2026 · 46 references
Pith's verdict: A useful integrated line test for BAO calibration, with a robust direct-catalogue offset, but the abstract oversells the transverse-specificity of ε.
T0 · AI review
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Referee report
The paper
The paper claims
Transverse BAO measurements carry a constant calibration error exactly degenerate with the product $r_{\rm d}h$, invisible to any transverse-only fit; the radial BAO sector breaks the degeneracy through an integrated geometric identity.
The reading
What carries the argument
The load-bearing object is the integrated consistency relation $T(z)=A+B X(z)$ (Eq. 4), obtained by integrating the flat-FLRW identity $D'_M(z)=D_H(z)$ after allowing for a constant relative calibration factor $\varepsilon$ in the angular BAO scale. Here $T(z)\equiv(180/\pi)/\theta_{\rm BAO}(z)$ is built from transverse measurements only and $X(z)\equiv\int_{z_0}^{z}(D_H/r_{\rm d})\,d\tilde z$ from radial measurements only, so the slope $B=1/\varepsilon$ measures the mutual calibration of the two sectors without any model for $H(z)$, $H_0$, $r_{\rm d}$, or the dark-energy equation of state. Because the relation is an identity in flat FLRW geometry, any constant departure from $B=1$ isolates a measurement-chain inconsistency rather than a cosmological one.
Extended reading notes
Core claim
The paper's central claim is that a constant calibration error in the transverse BAO scale is exactly degenerate with $r_{\rm d}h$: rescaling the angular BAO scale by a constant factor shifts the inferred $r_{\rm d}h$ by that factor, changes nothing else, and leaves $\chi^2$ unchanged, so no transverse-only cosmological fit can detect it, even when combined with external probes. To close this blind spot, the paper uses the flat-FLRW identity $D'_M(z)=D_H(z)$ to relate the two BAO sectors. Writing $\theta_{\rm BAO}(z)=\varepsilon r_{\rm d}/D_M(z)$ and defining $T(z)\equiv(180/\pi)/\theta_{\rm BAO}(z)$ and $X(z)\equiv\int_{z_0}^{z}(D_H/r_{\rm d})\,d\tilde z$, the identity becomes $T(z)=A+B X(z)$ with $B=1/\varepsilon$. The construction cancels $H_0$, $r_{\rm d}$, and the dark-energy equation of state, so a fitted slope with $\varepsilon\ne 1$ cannot be produced by any dark-energy model or by spatial curvature; it indicates a relative calibration or standard-ruler inconsistency in the measurement chain. Applied to the two leading published transverse compilations, the test yields $\varepsilon=1.073\pm0.021$ and $\varepsilon=1.021\pm0.029$, and a direct catalogue comparison shows the two disagree at $3.9\sigma$ with a constant-in-redshift offset; a companion check on the second compilation shows its published errors understate its own point-to-point scatter by $\sqrt{127.5/12}\simeq 3.3$.
Load-bearing premise
The radial BAO reference used to build X(z) is assumed to be free of a constant calibration error of its own; if the radial measurements carry a constant offset, that offset is absorbed into the fitted slope and masquerades as a transverse calibration error, making ε a relative rather than absolute calibration.
Editorial extensions
If this is right
- A constant transverse BAO calibration error cannot be detected by any parameter-level fit using those measurements alone; only the shape of $D_M(z)$, and hence $\Omega_m$, survives uncontaminated once the offset is constant.
- Published transverse BAO catalogues can disagree by several percent even when they trace the same physical ruler, so differences between two-dimensional and three-dimensional BAO tension claims must be checked at the catalogue level before being interpreted cosmologically.
- The straight-line test works as a data-level consistency check prior to parameter inference whenever transverse and radial BAO measurements overlap in redshift, and it can identify both a constant calibration offset and an underestimated error budget.
- A constant $\varepsilon$ is not degenerate with curvature or dark energy; curvature produces a redshift-growing term in this relation, so a constant offset specifically points to the measurement pipeline, such as a template inference bias.
Reading between the lines
- Future angular BAO surveys could use overlapping redshift shells analysed by independent pipelines as a cross-calibration sample: agreement at the observed scatter level would bound projection and template systematics, while a persistent constant offset would fingerprint a pipeline effect.
- If a template inference bias of the same kind as the 3.2% correction applied in one pipeline were also present in the uncorrected compilation, it would account for roughly 3.2 of the 5.4 percentage points separating the two catalogues, leaving a residual common offset worth testing by re-running the uncorrected sample through the corrected pipeline.
- The same integrated-consistency construction could be applied to photometric redshift calibration, since any uniform multiplicative error in the angular scale maps directly to $\varepsilon$; a null result would place sub-percent bounds on the combined imaging systematics of future surveys.
Original abstract
Transverse baryon acoustic oscillation (BAO) measurements are increasingly used for cosmological inference, and carry a calibration that no such inference can constrain. A constant error in the transverse BAO scale is exactly degenerate with the combination $r_{\rm d} h$: it leaves the goodness of fit unchanged and the recovered parameters plausible, and is therefore invisible to any analysis that uses these measurements alone. The radial BAO sector removes this degeneracy, supplying $D_{\rm M}/r_{\rm d}$ by integration without reference to $H_0$ or to any model for the expansion rate. In flat Friedmann--Lema\^itre--Robertson--Walker (FLRW) geometry the relation between the two sectors is an identity, so the sound horizon and the dark-energy equation of state cancel as well. An integrated form of this identity reduces the consistency test to a straight line, whose slope measures a relative transverse calibration $\varepsilon$. A departure from $\varepsilon = 1$ cannot be produced by any dark-energy model, nor by spatial curvature: it indicates an inconsistency in the measurement chain rather than in the cosmology. We apply the test to the two main SDSS transverse BAO compilations, which give $\varepsilon = 1.073 \pm 0.021$ and $1.021 \pm 0.029$. The first differs from unity at $3.8\sigma$ using the published independent errors, while the second is consistent with unity. The two compilations themselves differ by $(5.4 \pm 1.4)\%$, or $3.9\sigma$, and the offset is constant in redshift. The test provides a direct diagnostic for current and future angular BAO measurements.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Transverse baryon acoustic oscillation (BAO) measurements are increasingly used for cosmological inference, and carry a calibration that no such inference can constrain. A constant error in the transverse BAO scale is exactly degenerate with the combination $r_{\rm d} h$: it leaves the goodness of fit unchanged and the recovered parameters plausible, and is therefore invisible to any analysis that uses these measurements alone. The radial BAO sector removes this degeneracy, supplying $D_{\rm M}/r_{\rm d}$ by integration without reference to $H_0$ or to any model for the expansion rate. In flat Friedmann--Lema\^itre--Robertson--Walker (FLRW) geometry the relation between the two sectors is an identity, so the sound horizon and the dark-energy equation of state cancel as well. An integrated form of this identity reduces the consistency test to a straight line, whose slope measures a relative transverse calibration $\varepsilon$. A departure from $\varepsilon = 1$ cannot be produced by any dark-energy model, nor by spatial curvature: it indicates an inconsistency in the measurement chain rather than in the cosmology. We apply the test to the two main SDSS transverse BAO compilations, which give $\varepsilon = 1.073 \pm 0.021$ and $1.021 \pm 0.029$. The first differs from unity at $3.8\sigma$ using the published independent errors, while the second is consistent with unity. The two compilations themselves differ by $(5.4 \pm 1.4)\%$, or $3.9\sigma$, and the offset is constant in redshift. The test provides a direct diagnostic for current and future angular BAO measurements.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Transverse baryon acoustic oscillation (BAO) measurements are increasingly used for cosmological inference, and carry a calibration that no such inference can constrain. | background 0.78 | 0.09 | 0.26 | asserted 1.00 |
| s1 | A constant error in the transverse BAO scale is exactly degenerate with the combination $r_{\rm d} h$: it leaves the goodness of fit unchanged and the recovered parameters plausible, and is therefore invisible to any analysis that uses these measurements alone. | background 0.56 | 0.21 | 0.39 | asserted 1.00 |
| s2 | The radial BAO sector removes this degeneracy, supplying $D_{\rm M}/r_{\rm d}$ by integration without reference to $H_0$ or to any model for the expansion rate. | method 0.56 | 0.16 | 0.11 | asserted 1.00 |
| s3 | In flat Friedmann--Lema\^itre--Robertson--Walker (FLRW) geometry the relation between the two sectors is an identity, so the sound horizon and the dark-energy equation of state cancel as well. | method 0.57 | 0.22 | 0.08 | asserted 1.00 |
| s4 | An integrated form of this identity reduces the consistency test to a straight line, whose slope measures a relative transverse calibration $\varepsilon$. | method 0.87 | 0.52 | 0.11 | asserted 1.00 |
| s5 | A departure from $\varepsilon = 1$ cannot be produced by any dark-energy model, nor by spatial curvature: it indicates an inconsistency in the measurement chain rather than in the cosmology. | interpretation 0.95 | 0.28 | 0.36 | asserted 0.95 |
| s6 | We apply the test to the two main SDSS transverse BAO compilations, which give $\varepsilon = 1.073 \pm 0.021$ and $1.021 \pm 0.029$. | result 0.83 | 0.93 | 0.14 | asserted 1.00 |
| s7 | The first differs from unity at $3.8\sigma$ using the published independent errors, while the second is consistent with unity. | result 0.98 | 0.85 | 0.15 | asserted 0.96 |
| s8 | The two compilations themselves differ by $(5.4 \pm 1.4)\%$, or $3.9\sigma$, and the offset is constant in redshift. | result 1.00 | 0.89 | 0.19 | asserted 1.00 |
| s9 | The test provides a direct diagnostic for current and future angular BAO measurements. | interpretation 0.65 | 0.37 | 0.13 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:2608.20296 by the authors.
References
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 40 sentences without a confident label
Uses data or values from 8 papers
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Data.—We use the radial BAO measurements from the BOSS DR12 consensus [ref] at $z = 0.38, 0.51, 0.61$, together with DESI DR2 [ref] above $z = 0.61$.
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample · Introduction · 1.00
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Data.—We use the radial BAO measurements from the BOSS DR12 consensus [ref] at $z = 0.38, 0.51, 0.61$, together with DESI DR2 [ref] above $z = 0.61$.
DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints · Introduction · 1.00
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Menote & Marra (MM) [ref] provide 14 measurements over $0.35 ≤z ≤0.63$ from BOSS DR12 and eBOSS DR16, together with a published $14×14$ correlation matrix.
Baryon acoustic oscillations in thin redshift shells from BOSS DR12 and eBOSS DR16 galaxies · Introduction · 0.98
Cites as background 7 papers
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The standard three-dimensional (3D) BAO analysis converts angular and redshift coordinates into comoving coordinates using a fiducial cosmology and measures radial and transverse dilation factors [ref] .
The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations · Introduction · 0.95
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The standard three-dimensional (3D) BAO analysis converts angular and redshift coordinates into comoving coordinates using a fiducial cosmology and measures radial and transverse dilation factors [ref] .
Observational Probes of Cosmic Acceleration · Introduction · 0.95
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The standard three-dimensional (3D) BAO analysis converts angular and redshift coordinates into comoving coordinates using a fiducial cosmology and measures radial and transverse dilation factors [ref] .
The Baryon Oscillation Spectroscopic Survey of SDSS-III · Introduction · 0.95
Discussion
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