arxiv: 2604.11106 · v2 · submitted 2026-04-13 · 🌌 astro-ph.CO

Recognition: unknown

On the origin of the BAOtr-DESI tension

Ioannis Pantos , Leandros Perivolaropoulos

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:50 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords BAODESIBAOtrdark energyCPL parametrizationHubble tensioncosmological distancesdataset tension

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The pith

BAOtr and DESI BAO datasets cannot be fit simultaneously by any CMB-consistent CPL dark energy model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines why angular BAO measurements from thin redshift shells (BAOtr) prefer smaller comoving distance ratios than the DESI DR2 three-dimensional BAO data at redshifts below 0.65. It first confirms that the published DESI distances remain essentially independent of the fiducial cosmology, with residual effects below 0.3 percent. The authors then scan the two-parameter CPL dark energy model while enforcing the Planck theta-star constraint and optimizing other parameters to DESI. Both direct comparison and interpolation tests show an unavoidable trade-off: good fits to one dataset produce poor fits to the other. This leaves only two broad explanations for the observed mismatch.

Core claim

The published 3D BAO distances are fiducial-independent by construction with residuals at the 0.3 percent level. No model in the CPL parameter space that is consistent with Planck theta-star and fits DESI well can also accommodate the BAOtr data; the reverse also fails. The direct 3.7-sigma data-versus-data disagreement at z=0.510 cannot be removed by any smooth modification of D_M(z). These results remain stable when SDSS data replace DESI and across analysis choices.

What carries the argument

The CPL dark energy parametrization w(z)=w0+wa(1-a), used to jointly optimize Omega_m and H0 under the Planck theta-star constraint and test against both DESI and BAOtr distance ratios.

If this is right

Models with chi-squared_DESI below or equal to 5 produce chi-squared_BAOtr above or equal to 42.
Reducing the BAOtr tension to chi-squared approximately 37 forces chi-squared_DESI above or equal to 8.
The 3.7-sigma mismatch at z=0.510 sets an irreducible floor that no smooth D_M(z) adjustment can remove.
The conclusions hold after substituting SDSS for DESI and across extrapolation schemes.
The remaining possibilities are observational systematics or new physics beyond the CPL form.

Where Pith is reading between the lines

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

If BAOtr measurements are shown to be free of systematics, 3D BAO pipelines may contain unaccounted reconstruction effects beyond fiducial choice.
Future surveys could routinely cross-check angular and 3D BAO at the same redshifts to isolate such dataset tensions.
If systematics are ruled out, dark energy models with non-smooth or scale-dependent features would need explicit testing.

Load-bearing premise

The CPL parametrization is flexible enough to describe any smooth dark energy evolution consistent with the data.

What would settle it

A reanalysis or new measurement of the comoving distance ratio at z=0.510 that brings BAOtr and DESI into agreement within 2 sigma after all fiducial corrections.

Figures

Figures reproduced from arXiv: 2604.11106 by Ioannis Pantos, Leandros Perivolaropoulos.

**Figure 2.** Figure 2: Trade-off between χ 2 DESI and χ 2 BAOtr (Method A) across the DESI-optimized, CMB-consistent CPL parameter space. Each point represents a (w0, wa) model with (Ωm, H0) set by Eqs. (12)–(13), coloured by w0. The black star marks ΛCDM; the magenta circle CMB+PP&SH0ES; the red square CMB+DESI. Dotted lines show the expected χ 2 for consistency. No CPL model reaches the lower-left corner. χ 2 summary [PITH_FU… view at source ↗

**Figure 3.** Figure 3: Left: χ 2 BAOtr(w0, wa) (Method A, DESI-optimized). Green: low tension. Right: χ 2 DESI(w0, wa). Light: low χ 2 . The two surfaces have opposite gradients, confirming the trade-off. Symbols mark published posteriors as in [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗

**Figure 4.** Figure 4: Per-point tension Ti (Method B, ΛCDM) using DESI anchors (blue) and SDSS anchors (red). Both produce the same pattern. The tension is a generic feature of the BAOtr–BAO 3D comparison. 5.4. Consistency between methods [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗

**Figure 5.** Figure 5: Residuals ∆(DM/rd) relative to Planck ΛCDM (Ωm = 0.3153, H0 = 67.36 km s−1 Mpc−1 ). DESI data (red circles) and BAOtr data (green squares) are shown with their 1σ uncertainties. The pink shaded region (z < 0.295) marks the zone below the lowest DESI anchor, where Method B predictions depend on the extrapolation scheme. Left (Method A): Planck ΛCDM defines the zero line (black solid; χ 2 BAOtr = 59, χ 2 DE… view at source ↗

read the original abstract

The fiducial-independent angular/transverse BAO dataset, obtained from two-point angular correlation functions in thin redshift shells (hereafter BAOtr), systematically prefers smaller comoving distance ratios $D_{\rm M}/r_{\rm d}$ than the DESI DR2 three-dimensional BAO measurements at $z \lesssim 0.65$, driving dataset-dependent CPL dark-energy inferences and conflicting conclusions about the Hubble tension. We investigate whether this disagreement can be attributed to the $\Lambda$CDM fiducial assumed in the 3D BAO pipeline, or resolved within the CPL parametrisation. We show that the published 3D BAO distances are fiducial-independent by construction, with residual effects at $\lesssim 0.3\%$ -- negligible against the 10--18\% BAOtr uncertainties. We then scan the CPL parameter space with $\Omega_m$ and $H_0$ jointly determined at each $(w_0, w_a)$ by the Planck $\theta_*$ constraint and optimisation against the DESI data. Two complementary tests are performed: a direct comparison of each DESI-optimized model with the BAOtr data, and an $\alpha$-interpolation test that anchors the prediction to the DESI measurements. Both reveal an inescapable trade-off: models that fit DESI well ($\chi^2_{\rm DESI} \lesssim 5$) yield $\chi^2_{\rm BAOtr} \gtrsim 42$, while reducing the BAOtr tension to $\chi^2_{\rm BAOtr} \sim 37$ requires $\chi^2_{\rm DESI} \gtrsim 8$. No CMB-consistent CPL model fits both datasets simultaneously. The direct comparison at $z = 0.510$ -- where BAOtr and DESI disagree by $3.7\sigma$ (data-versus-data) -- sets an irreducible tension floor that no smooth modification of $D_{\rm M}(z)$ can remove. These conclusions are robust across analysis methods, extrapolation schemes, and substitution of SDSS for DESI. The remaining explanations are observational systematics -- most plausibly in the BAOtr measurements -- or new physics beyond CPL.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows a direct 3.7-sigma data-versus-data offset at z=0.51 between BAOtr and DESI that CPL models cannot reconcile without a clear chi-squared trade-off.

read the letter

The paper shows that the BAOtr and DESI datasets disagree at the 3.7-sigma level in a model-independent way at z=0.51, and that no CPL dark energy model consistent with Planck can fit both without paying a steep chi-squared price on one dataset or the other. The authors also confirm that residual fiducial dependence in the published DESI distances sits below 0.3 percent, well under the BAOtr uncertainties. This is the core result worth noting first. The work does a clean job of quantifying the trade-off through CPL scans optimized to DESI plus Planck theta-star, then testing against BAOtr. The alpha-interpolation test is a practical addition that anchors predictions straight to the DESI points. Both methods give the same picture: chi-squared below 5 on DESI pushes BAOtr above 42, while bringing BAOtr down to around 37 forces DESI above 8. The direct comparison at one redshift supplies the irreducible floor claim, and the robustness checks with SDSS substitution add some weight. The soft spots are modest but real. The assertion that no smooth DM(z) modification can remove the tension rests primarily on that single-redshift inconsistency holding up. If the BAOtr errors or the DESI measurements carry unaccounted systematics, the floor could shift. The paper flags observational systematics in BAOtr as the leading remaining possibility, which is fair, but the quantitative chi-squared floors would be easier to assess with more explicit error propagation details. This is for cosmologists tracking BAO dataset comparisons and the Hubble tension. A reader who wants concrete numbers on how different BAO analyses pull against each other will get value from the trade-off plots and the fiducial check. It deserves a serious referee because the tests are targeted, the incompatibility is stated with specific values, and the conclusions are falsifiable even if the ultimate cause turns out to be systematics rather than new physics. I would send it to peer review.

Referee Report

1 major / 2 minor

Summary. The manuscript claims that the BAOtr angular BAO dataset and DESI DR2 3D BAO measurements exhibit an irreducible tension, most notably a 3.7σ discrepancy in D_M/r_d at z=0.510. After demonstrating that residual fiducial dependence in the published DESI distances is ≲0.3% (negligible compared to BAOtr uncertainties), the authors perform CPL parameter scans with Ω_m and H_0 fixed by the Planck θ_* constraint plus optimization to DESI. Both direct model-to-BAOtr comparisons and an α-interpolation test show an inescapable χ² trade-off: good DESI fits (χ²_DESI ≲5) produce χ²_BAOtr ≳42, while acceptable BAOtr fits require χ²_DESI ≳8. No CMB-consistent CPL model accommodates both datasets simultaneously, and the single-redshift data-versus-data inconsistency sets a floor that no smooth D_M(z) modification can remove. The conclusions are stated to be robust to analysis choices and to substitution of SDSS for DESI.

Significance. If the central result holds, the work is significant for BAO cosmology and the Hubble tension debate: it rules out fiducial-cosmology artifacts and standard CPL dark-energy evolution as explanations for the BAOtr–DESI mismatch, thereby focusing attention on possible observational systematics (most plausibly in BAOtr) or physics beyond CPL. The explicit χ² scans, the model-independent 3.7σ datum at z=0.510, and the α-interpolation test that anchors predictions directly to DESI constitute concrete, falsifiable evidence rather than a circular fit. The demonstration that the published DESI distances are effectively fiducial-independent at the 0.3% level is a useful technical clarification for the community.

major comments (1)

[Results section on α-interpolation test] The assertion that 'no smooth modification of D_M(z) can remove' the tension floor is load-bearing for the final conclusion. While the 3.7σ data-versus-data discrepancy at z=0.510 is model-independent, the extrapolation to arbitrary smooth D_M(z) rests on the CPL scans plus the α-interpolation test. A brief explicit statement of the functional form assumed for the interpolation (or the range of α values explored) would make this step fully transparent.

minor comments (2)

[Abstract and main results paragraphs] The specific χ² thresholds (χ²_DESI ≲5, χ²_BAOtr ≳42, etc.) are quoted without accompanying degrees of freedom or reduced-χ² values; adding these would allow readers to judge the absolute goodness of fit.
[Discussion of robustness] A short table or figure panel comparing the best-fit CPL parameters and χ² values when SDSS is substituted for DESI would make the robustness statement more quantitative.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the positive overall assessment. The recommendation for minor revision is welcome, and we address the single major comment below.

read point-by-point responses

Referee: [Results section on α-interpolation test] The assertion that 'no smooth modification of D_M(z) can remove' the tension floor is load-bearing for the final conclusion. While the 3.7σ data-versus-data discrepancy at z=0.510 is model-independent, the extrapolation to arbitrary smooth D_M(z) rests on the CPL scans plus the α-interpolation test. A brief explicit statement of the functional form assumed for the interpolation (or the range of α values explored) would make this step fully transparent.

Authors: We agree that an explicit description of the interpolation procedure will improve transparency. The α-interpolation test anchors the predicted D_M(z) to the DESI measurements at the observed redshifts and uses a smooth, monotonic interpolation whose deviation amplitude is controlled by the parameter α. In the revised manuscript we will insert a concise statement specifying the functional form (a linear interpolation in the scaled comoving distance ratio) and the range of α explored (chosen to span the plausible domain for smooth modifications consistent with the CPL framework). This clarification does not alter the reported results or conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim from direct data comparison

full rationale

The derivation proceeds via explicit CPL parameter scans optimized jointly to Planck θ* and DESI data, followed by independent χ² evaluation against BAOtr and an α-interpolation test that anchors predictions directly to DESI measurements. The fiducial-independence argument rests on the published pipeline construction (residuals ≲0.3%) rather than any self-fit. No step reduces a prediction to its own input by definition, no load-bearing self-citation chain is invoked for uniqueness, and the 3.7σ z=0.510 discrepancy is a raw data-versus-data comparison. This is the normal non-circular case for a data-driven tension analysis.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard CPL form for dark energy, the Planck theta-star constraint, and the assumption that published DESI distances are effectively fiducial-independent. No new entities are introduced.

free parameters (4)

w0
CPL dark energy parameter scanned over a grid and optimized against DESI data.
wa
CPL dark energy parameter scanned over a grid and optimized against DESI data.
Omega_m
Jointly determined at each (w0, wa) by Planck theta* and DESI optimization.
H0
Jointly determined at each (w0, wa) by Planck theta* and DESI optimization.

axioms (2)

domain assumption CPL parametrization w(z) = w0 + wa z/(1+z) is adequate to describe any relevant smooth dark energy evolution.
Invoked throughout the parameter scan and model comparison sections.
domain assumption Planck theta* constraint provides a valid external anchor for Omega_m and H0 at each CPL point.
Used to reduce the parameter space before comparing to BAO datasets.

pith-pipeline@v0.9.0 · 5713 in / 1510 out tokens · 54706 ms · 2026-05-10T15:50:55.626909+00:00 · methodology

discussion (0)

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