REVIEW 3 major objections 5 minor 10 cited by
Baryon Acoustic Oscillations from a Different Angle
T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash
Pith's one-line read In rotated coordinates, DESI DR2 BAO data move into line with Planck ΛCDM; no significant evidence for evolving dark energy remains.
desk verdict A clean rotated-coordinate diagnostic shows DESI DR2 BAO are more Planck-ΛCDM-friendly than DR1, but the paper's stronger 'no evidence for evolving dark energy' conclusion is a prior-dependent judgment, not an empirical fact. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is a rotation of the two BAO observables $D_M/r_d$ and $D_H/r_d$ into orthogonal combinations $D_{\rm perp}$ and $D_{\rm par}$, with a rotation angle $\gamma(z)$ chosen at each effective redshift so that the Planck ΛCDM degeneracy line (fixed by the tight constraint on $\Omega_m h^3$) becomes horizontal. In this frame $D_{\rm perp}$ is predicted by Planck with negligible error, so agreement with ΛCDM is settled by a single number with no nuisance parameters or priors, while $D_{\rm par}$ maps linearly onto the physical matter density through $\omega_m = 0.14205 + \beta\,(D_{\rm par} - D_{\rm par}^{\rm Planck})$. A second rotation acts in theory space: replacing $(w_0, w_a)$ by $(w_{\rm piv}, w_a)$ with $w_{\rm piv} = w(z_{\rm piv})$ at $z_{\rm piv}\approx 0.5$ decorrelates the two dark-energy parameters, showing that the pivot equation-of-state is tightly constrained and consistent with a cosmological constant.
What would settle it
If a future BAO data set (e.g., DESI DR3) finds the LRG1 $D_{\rm perp}$ value falling below its DR2 value of $5.08\pm0.37$ and the pivot equation-of-state $w(z=0.5)$ moving more than about 2σ away from $-1$ in a joint BAO+CMB fit, the paper's conclusion that DR2 moved toward Planck ΛCDM with no evidence for evolving dark energy would be contradicted.
Extended reading notes
Core claim
The central claim, stated on the paper's own terms, is that the DESI DR2 BAO measurements 'move closer towards the expectations of Planck ΛCDM' compared with DR1, and that from the comparison of Planck and DESI BAO measurements 'we find no significant evidence in support of evolving dark energy.' The analysis defines the two rotated distance ratios $D_{\rm perp}$ and $D_{\rm par}$, chosen so that Planck's ΛCDM prediction for $D_{\rm perp}$ is essentially a delta function at every effective redshift. For the two low-redshift luminous-red-galaxy samples that showed the largest DR1 discrepancy, the $D_{\rm perp}$ residuals shift from 2.5σ and -0.5σ in DR1 to 1.8σ and 1.4σ in DR2. The $D_{\rm par}$ data translate into a matter density $\omega_m = 0.13909 \pm 0.00073$ averaged over all redshifts, about 2.1σ below the Planck value, and the extension to the $w_0$–$w_a$ parametrization yields $w(z=0.5) = -0.996 \pm 0.046$ when DESI BAO and the compressed CMB likelihood are combined. The paper also shows that reparameterizing the dark-energy model to a pivot redshift decorrelates $w_0$ and $w_a$, exposing why the DESI collaboration's quoted significance, based on $\Delta\chi^2_{\rm MAP}=-8.0$, overstates the case for evolving dark energy.
Load-bearing premise
The central conclusion rests on a subjective prior that judges evolving-dark-energy models as much less plausible than the cosmological constant before the data are examined; the paper explicitly concedes that the size of this penalty is entirely subjective, and without it the DESI data improve the fit by $\Delta\chi^2 = -8.0$.
Editorial extensions
If this is right
- If the rotated-variable analysis is correct, DESI DR2 BAO data are consistent with the Planck ΛCDM cosmology at all effective redshifts from $z\approx 0.5$ to $z\approx 2.3$, with the two LRG samples that previously showed tension moving into line.
- The matter density inferred from $D_{\rm par}$, averaged over all DESI samples, is $\omega_m = 0.13909 \pm 0.00073$, about 2.1σ below Planck, implying mild tension remains only in the parallel direction.
- In the $w_0$–$w_a$ extension, the pivot equation-of-state is $w(z=0.5) = -0.996 \pm 0.046$, so the data are compatible with a cosmological constant at the pivot despite the large $w_a$ uncertainty.
- The DESI team's '3.1σ' preference for evolving dark energy from DESI BAO + CMB is not a robust probability: it follows from $\Delta\chi^2_{\rm MAP}=-8.0$ treated as a chi-squared statistic without a prior penalty, and the paper argues a physically motivated prior would eliminate the preference.
- Adding alternative CMB data (ACT) does not strengthen the case for evolving dark energy, and some Planck+ACT combinations weaken it (as the paper cites from Garcia-Quintero et al. 2025).
Reading between the lines
- A direct test of the trend: if the DESI DR3 release finds the LRG1 $D_{\rm perp}$ central value below its DR2 value of $5.08\pm0.37$, the convergence toward Planck seen in DR2 would look like a statistical fluctuation rather than a systematic improvement.
- The same rotation construction depends only on the Planck-ΛCDM degeneracy direction, so it can be applied unchanged to future BAO surveys to provide a near-model-free consistency check with the CMB.
- If the paper's Bayesian-prior argument is right, the burden shifts to dark-energy model builders: to make a convincing case for evolving dark energy, the combined data would need to produce a much larger $\Delta\chi^2$ improvement than $-8$, or the field would need a principled theoretical prior for $w_0$–$w_a$ models.
- The appendix's worsening DES5Y-versus-DESI/Planck tension suggests that the '4σ' claims quoted from combining DES5Y supernovae with DESI BAO are dominated by the supernova sample rather than by dark energy; recalibrating the DES5Y low-redshift photometry should remove or confirm that tension.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes a rotated-coordinate analysis of DESI BAO distance measurements, defining orthogonal quantities D_perp and D_par from DM/rd and DH/rd. The author argues that, under Planck LCDM, D_perp is predicted with negligible uncertainty, allowing a clean consistency test of DESI DR1 and DR2 against Planck. The paper reports that DESI DR2 D_perp measurements are in better agreement with Planck LCDM than DR1, that D_par converts to constraints on omega_m that remain consistent with Planck, and that a rotated w0-wa analysis gives w(z=0.5) = -0.996 +/- 0.046. The paper further critiques the DESI collaboration's use of Delta-chi^2_MAP as evidence for evolving dark energy, arguing that the evidence is prior-dependent, and includes an appendix comparing DES5Y supernova constraints with DESI and Planck.
Significance. The D_perp statistic is a useful, transparent consistency test, and the analytic Gaussian marginalization is straightforward and reproducible from the quoted DESI and Planck results. The paper also makes a valid and important methodological point: Delta-chi^2_MAP with a uniform prior in (w0, wa) is not a model-independent measure of evidence for evolving dark energy. If the quantitative claims are brought in line with the tables, the rotated-coordinate framework could be a valuable addition to the BAO literature. However, the paper's headline statements currently outrun the tabulated results in a few places, and the omega_m conversion needs an error-propagation check.
major comments (3)
- [Section 2 and Table 1] The statement that the 2025 DESI data are 'more consistent with LCDM' for both LRG samples is not supported by Table 1. For LRG2, D_perp moves from 9.54 +/- 0.60 (DR1) to 8.76 +/- 0.34 (DR2), with the Planck value at 9.22; the absolute residual grows from 0.32 to 0.46 and the two-tailed p-value worsens from 0.60 to 0.16. The abstract and Section 4 should either restrict the 'moves closer' claim to LRG1 and to the full redshift set, or explicitly justify why the worsening LRG2 p-value is not the relevant comparison.
- [Section 3 and Abstract] The conclusion that there is 'no significant evidence in support of evolving dark energy' is prior-dependent rather than an empirical finding. The paper reports Delta-chi^2_MAP = -8.0 for w0waCDM relative to LCDM, and the rotated posterior gives wa = -1.78 +/- 0.79, about 2.3 sigma from zero; the conclusion relies on a subjective prior penalty whose size is conceded in the text to be 'entirely subjective.' The abstract and conclusions should state this conditionality explicitly, for example by saying 'under the Bayesian prior penalty adopted here.'
- [Section 2, Eq. (7), and Table 2] The conversion of D_par measurements into omega_m constraints does not propagate the uncertainty in the slope beta or in the Planck reference value D_par^Planck. Table 2 lists Planck D_par uncertainties of order 0.1, which, when multiplied by beta ~ 0.009, contribute about 0.001 to omega_m, comparable to the quoted DESI omega_m errors of ~0.0015. The reported omega_m errors and the ~2.1 sigma average tension with Planck should be revised to include these terms, or the paper should justify that they are negligible.
minor comments (5)
- [Figure 4 caption] The caption describes red and blue contours as 'Pantheon+ (red) and DES5Y (blue) SN compilations,' but the text in Section 3 describes the red contours as DESI-DR2 BAO and DESI+QCMB; the caption should be corrected to match the text.
- [Section 4] The phrase 'as shown in the lower panel of Fig. 2' refers to the D_par results, but the lower panel of Fig. 3 contains the omega_m plot; the figure reference should be corrected.
- [Table 1] The table should state the sign convention for N_sigma; the listed values are consistent with N_sigma = (D_perp^Planck - D_perp^DESI)/sigma, but this is not stated explicitly in the caption.
- [Throughout] There are minor typographical errors, including 'perpendiclular' for 'perpendicular' and 'distrbution' for 'distribution,' which should be corrected in a revised version.
- [Eq. (5)] The exponent is printed as -a11 + a12^2/(4a22); while this is algebraically correct after marginalization, the plus sign inside the exponent may confuse readers, so a one-line derivation or a clarifying note would help.
Circularity Check
No significant circularity: the D_perp/D_par rotated-coordinate comparison is a self-contained consistency test against external DESI and Planck data, and the 'no evolving dark energy' conclusion is prior-dependent but not forced by construction.
full rationale
The central derivation is not circular. Dperp and Dpar are orthogonal linear combinations of the standard DESI observables DM/rd and DH/rd (Eqs. 4a-4b), with rotation angles gamma(z) fixed by the effective redshift and by the requirement that the Planck LCDM degeneracy line be horizontal. The Planck predictions for Dperp come from the external Planck TTTEEE chains, while the DESI Dperp values come from the external DESI DR1/DR2 measurements; the comparison is a projection of independent data onto a direction chosen from Planck, not an input recycled as a prediction. The Dpar-to-omega_m conversion (Eq. 7) is a calibration on the Planck chains, but the DESI Dpar values are independent, so agreement or tension is informative and not guaranteed by construction. The w0-wa pivot analysis is a standard reparameterization of the same DESI+QCMB likelihood; reporting wpiv = -0.996 +/- 0.046 is a faithful summary of the fit, not a hidden re-importation of the conclusion. The paper's 'no significant evidence for evolving dark energy' wording does depend on a subjective Bayesian penalty ('How big a penalty is entirely subjective', Sec. 3) and on Delta chi2_MAP = -8.0 being reinterpreted; that is a statistical-philosophy limitation, not circularity. Some claims, such as the LRG2 Dperp 'moving closer' (Table 1 shows the p-value worsening from 0.60 to 0.16), are stronger than the tabulated numbers support, but this is an internal-consistency and robustness concern, not a circular-derivation concern. Minor self-citations (Efstathiou & Gratton 2021 for the Planck degeneracy line; Efstathiou 2025 for priors and DES5Y photometry) are not load-bearing: the degeneracy line can be verified from the Planck chains, and the priors can be replaced without changing the geometric comparison.
Assumptions & free parameters
free parameters (2)
- Rotation angles gamma(z) =
0.816, 0.500, 0.243, 0.0274, -0.0177, -0.0991 rad (Table 1)
- Calibration slope beta(z) in Eq. 7 =
0.00836 to 0.00975 (Table 2)
assumptions (4)
- domain assumption Spatial flatness (Omega_K = 0)
- domain assumption DESI likelihood is approximately Gaussian
- domain assumption Compressed CMB likelihood QCMB from DESI-DR2 is adequate
- ad hoc to paper Subjective prior penalty for w0-wa models
Cite this review
Pith. "Pith review of Baryon Acoustic Oscillations from a Different Angle." pith.science (2026). https://pith.science/paper/QWK7OHJE
@misc{pith2026250502658,
author = {Pith},
title = {Pith review of: Baryon Acoustic Oscillations from a Different Angle},
year = {2026},
howpublished = {\url{https://pith.science/paper/QWK7OHJE}},
note = {Machine review of arXiv:2505.02658}
}
read the original abstract
This paper presents an alternative way of analysing Baryon Acoustic Oscillation (BAO) distance measurements via rotations to define new quantities Dperp and Dpar. These quantities allow simple tests of consistency with the Planck LCDM cosmology. The parameter Dperp is determined with negligible uncertainty from Planck under the assumption of LCDM. Comparing with measurements from the Dark Energy Spectroscopic Instrument (DESI), we find that the measurements of Dperp from Data Release 2 (DR2) move into significantly better agreement with the Planck LCDM cosmology compared to DESI Data Release 1 (DR1). The quantity in the orthogonal direction Dpar provides a measure of the physical matter density omega_m in the LCDM cosmology. The DR2 measurements of Dpar remain consistent with Planck LCDM despite the substantial improvement in their accuracy compared to the earlier DR1 results. From the comparison of Planck and DESI BAO measurements, we find no significant evidence in support of evolving dark energy. We also investigate a rotation in the theory space of the w_0 and w_a parameterization of the dark energy equation-of-state w(z). We show that the combination of DESI BAO measurements and the CMB constrain w(z=0.5) = -0.996 pm 0.046, i.e. very close to the value expected for a cosmological constant. We present a critique of the statistical methodology employed by the DESI collaboration and argue that it gives a misleading impression of the evidence in favour of evolving dark energy. An Appendix shows that the cosmological parameters determined from the Dark Energy Survey 5 Year supernova sample are in tension with those from DESI DR2 and parameters determined by Planck.
Figures
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Forward citations
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Reviewed August 16, 2026 · model on record in the stance chip above.
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