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arxiv: 2606.30527 · v1 · pith:5YMHPUKGnew · submitted 2026-06-29 · 🌌 astro-ph.CO

Universal distance modes from DESI BAO and Type Ia supernovae: what do cosmological rulers actually measure?

Matias Zaldarriaga This is my paper

Pith reviewed 2026-06-30 04:38 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords BAOType Ia supernovaecosmological distancesOmega_m h^2SVD decompositionLCDM extensionsdark energyspatial curvature
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The pith

The leading direction in DESI BAO and supernova distance data measures Omega_m h^2 and carries the tension with CMB predictions.

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

The paper decomposes low-redshift distance measurements from DESI baryon acoustic oscillations and three Type Ia supernova compilations using singular value decomposition. It shows that the strongest linear direction isolated by this method corresponds closely to the parameter combination Omega_m h^2. Baryon acoustic oscillation data constrain this combination more tightly than cosmic microwave background observations, while the supernova compilations provide weaker constraints. Across several extensions of the standard cosmological model, this same direction accounts for most of the observed discrepancy with cosmic microwave background-anchored predictions.

Core claim

The leading linear direction V_0, whose amplitude is denoted c_0, is to high accuracy a measurement of Omega_m h^2. The projection of the data onto V_0 essentially probes this single combination of parameters derived from the cosmic microwave background. Baryon acoustic oscillation measurements constrain the parameter more tightly than the cosmic microwave background itself, whereas the three supernova compilations do not. In every extension of the standard model examined, V_0 remains the leading measurable direction and contains most of the tension with cosmic microwave background predictions.

What carries the argument

Singular value decomposition of the low-redshift distance measurements, which isolates the leading linear directions in the data and maps their amplitudes to specific cosmological parameter combinations.

If this is right

  • In the w0-wa extension of the standard model a second measurable direction appears that tests dynamical dark energy independently, and the data show no significant tension in that direction.
  • Spatial curvature is the only other extension that opens a genuinely new measurable direction, and only marginally for baryon acoustic oscillation data.
  • Both measurable directions in the curvature extension independently favor positive spatial curvature, although the second direction remains poorly constrained.
  • The leading direction V_0 stays dominant in all considered extensions and continues to host the primary tension with cosmic microwave background predictions.

Where Pith is reading between the lines

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

  • Future surveys could target tighter measurements of this specific parameter combination to resolve or confirm the reported tension.
  • The result suggests that apparent cosmological tensions may concentrate in measurements of Omega_m h^2 rather than requiring wholesale revision of the underlying model.
  • If the mapping from data directions to parameters holds, analyses of combined datasets should prioritize checking consistency in this leading direction before interpreting broader parameter shifts.

Load-bearing premise

The singular value decomposition applied to the distance data accurately isolates linear directions that correspond directly to individual cosmological parameters such as Omega_m h^2 without substantial mixing from nonlinear effects, unmodeled systematics, or covariance errors.

What would settle it

A direct computation showing that the amplitude c_0 extracted from the data deviates significantly from the Omega_m h^2 value inferred from the cosmic microwave background, or that adding nonlinear corrections or revised covariances alters which direction emerges as leading.

Figures

Figures reproduced from arXiv: 2606.30527 by Matias Zaldarriaga.

Figure 3
Figure 3. Figure 3: All three SN datasets (mean-subtracted, binned to Union3 grid) vs. the ACT ΛCDM 1σ prediction envelope. Red circles: Union3 (22 bins). Blue squares: Pantheon+ (22 bins). Green triangles: DES-Dovekie (19 bins). The ACT band is narrow (∆µ ≲ 0.01 mag) because ACT tightly constrains Ωmh 2 . ratio reduce to z, so deviations from unity at low z are small. The lowest DESI data point at DM/DH = 1.04 deviates from … view at source ↗
Figure 2
Figure 2. Figure 2: Anisotropic distance ratio (DM/DH) for DESI DR2 BAO compared to ACT ΛCDM predictions, relative to the Planck reference. The blue band shows the 1σ ACT range. This ratio is insensitive to the overall distance scale (both DM and DH share the same rd calibration). The lowest-redshift point deviates from the low-z limit, the fea￾ture that would force a rapid evolution of w(z) in a fit. combined dark-matter dar… view at source ↗
Figure 4
Figure 4. Figure 4: c0 family of curves in observed space. Left: BAO DV /rd ratio (normalized to the Planck reference cosmology) for five values of c0 spanning ±5 whitened units (≈ ±3σ of the ACT chain). Black points: DESI DR2. Right: SN distance modulus residuals ∆µ (mean-subtracted) for the same c0 range. Points: DES-Dovekie. The c0 normalization differs between panels (Eq. 7): BAO c0 = 5 corresponds to a ∼ 5× larger Ωmh 2 … view at source ↗
Figure 5
Figure 5. Figure 5: Per-probe c0 distributions. Shaded regions: CMB chain predictions (model uncertainty in each probe’s c0). Dashed curves: measurement likelihoods centered at the data c0 value (σ = 1 in whitened space by construction). The BAO chain distribution (shaded, wide) has σc0 = 1.56, wider than the measurement likelihood, reflecting BAO’s ability to constrain Ωmh 2 beyond the CMB prior. The three SN chain distribut… view at source ↗
Figure 6
Figure 6. Figure 6: Effective Ωmh 2 measurements from all four dis￾tance probes, derived from c0 via the β-vector inversion (Eq. 8). Error bars show total uncertainty (measurement + marginalization over Ωbh 2 and θ⋆, added in quadrature). The gray band shows the ACT ΛCDM posterior width. BAO provides a tighter constraint than the CMB. 4.3. Goodness of Fit and Robustness Beyond the c0 tension, a natural question is whether the… view at source ↗
Figure 7
Figure 7. Figure 7: Hubble rate ratio H(z)/Href(z) for varying Ωmh 2 at fixed θ⋆ (flat ΛCDM). Higher Ωmh 2 (blue, dashed) raises H at high z but lowers H0; the crossover near z ∼ 2 falls within the DESI BAO range (shaded). The red curve shows the BAO-implied Ωmh 2 from the c0 measurement (Ωmh 2 = 0.139, H0 = 70.6). content to the Planck ΛCDM best-fit (Ωmh 2 = 0.1424, Ωbh 2 = 0.02237) and compute BAO and SN observ￾ables on a 1… view at source ↗
Figure 8
Figure 8. Figure 8: shows contours of constant c0 and c1 in the (w0, wa) plane for BAO and Union3. Several features are immediately apparent: • Contours are straight: Over most of the pa￾rameter space the contours are relatively straight, which means each of these variables measures the equation of state at a specific pivot redshift. • The spacing of the contours differs: The spac￾ing encodes how measurable the parameter is a… view at source ↗
Figure 9
Figure 9. Figure 9: Planck+DESI w0–wa chain SN prediction (gray band, ±1σ) vs. all three SN datasets. Each dataset is inde￾pendently shifted by its optimal display offset Mdisp (zero χ 2 cost due to MB marginalization). 7.5 5.0 2.5 0.0 2.5 5.0 7.5 c1 (Union3 basis) 0.0 0.1 0.2 0.3 0.4 Density w0wa chain ( c1 =-3.0) Union3: a1=-1.5 Pantheon+: a1=+0.2 (/1.13) DES-Dovekie: a1=-0.7 (/1.01) CDM [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 10
Figure 10. Figure 10: SN c1 (dark energy mode). Gray histogram: Planck+DESI w0–wa chain prediction (⟨c1⟩ ≈ −3). Dashed Gaussians: data measurements a1 from each SN dataset (unit measurement uncertainty). All datasets are rescaled to the Union3 c1 basis (proportionality factors: c P+ 1 ≈ 1.13 c U3 1 , c DES 1 ≈ 1.01 c U3 1 ). All three lie much closer to a1 = 0 than to the chain prediction, collectively displaced from it [PITH… view at source ↗
Figure 11
Figure 11. Figure 11: BAO data-centered reconstruction bands. Bands centered on data projections aα with unit-Gaussian width per mode. Four levels: c0 only (dotted), c0+c1 (dashed), c0+c1+c2 (dash-dot), c0+c1+c2+c3 (solid). Gray: full w0–wa chain ±1σ. The DV dip at z ∼ 0.5–1.0 emerges when c2 and c3 are included. Using the ACT chain in which Ωk is varied, we regress the chain values of c0 on (Ωmh 2 , Ωk) — the same pro￾cedure … view at source ↗
Figure 12
Figure 12. Figure 12: SVD χ 2 analysis in the (w0, wa) plane vs. the Planck+DESI chain posterior. (A) 2-mode SVD (blue) does not match chain (red). (B) 4-mode SVD closely matches. (C) c2 colormap: the chain occupies a region of large |c2|. (D) c3 colormap: the chain’s c3 is consistent with the data. The point: four SVD modes reproduce the chain posterior, and the chain’s displacement from ΛCDM is carried by c0 and c2, not by t… view at source ↗
Figure 13
Figure 13. Figure 13: w(zpivot) distributions. Colored histograms: Planck+DESI w0–wa chain. Black dashed: data measurement from cα projection (Gaussian with σw = 1/|aα|; for c0, σ includes Ωmh 2 marginalization). Left: c0 pivot (z = 0.74)—w ̸= −1, but this is the c0 direction, which is affected by Ωmh 2 . Center: BAO c1 pivot (z = 0.46)—consistent with ΛCDM. Right: SN c1 pivot (z ≈ 0)—the chain predicts w ≈ −0.3 but SN data gi… view at source ↗
Figure 14
Figure 14. Figure 14: BAO c0 distributions for ΛCDM (red) and Ωk (blue) ACT chains, with DESI data (black dashed). The Ωk distribution is much broader because the CMB geometric degeneracy allows H0 ∈ [55, 68] km s−1 Mpc−1 . The broad￾ening does not offset the larger offset of the chain mean from the data, so allowing curvature slightly increases the BAO c0 tension (2.2σ → 2.6σ). tude on Mpc scales, which clump baryons and mod￾… view at source ↗
Figure 15
Figure 15. Figure 15: BAO c0 distributions under beyond-ΛCDM extension chains. Blue: ACT ΛCDM. Colored: extension chains projected onto the same c0 direction. Red dashed: DESI data (σ = 1). The right panel shows Union3 for comparison. The point: freeing Alens or BPMF broadens and shifts the predicted c0 toward the data and so reduces the BAO tension, whereas EDE leaves it essentially unchanged. tal limitation of distance measu… view at source ↗
Figure 16
Figure 16. Figure 16: Proxy observables as a function of each CMB parameter (in units of σp from the ACT chain). Left: BAO proxy DM(0.5)/rd. Right: SN proxy DM(0.3)/DM(0.5). All curves computed at fixed θ⋆ (solving for H0), except the θ⋆ curve which varies the angular scale constraint. The slope at the origin times σp/⟨p⟩ gives fp ( [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
read the original abstract

We use an SVD decomposition of the low-redshift distance measurements from DESI BAO and three Type Ia supernova compilations to identify the leading linear directions probed by the data and to localize the tension with the LCDM CMB-anchored predictions. The leading direction V_0 -- whose data amplitude we denote c_0 -- is, to high accuracy, a measurement of Omega_m h^2: the projection of the data on V_0 probes essentially this one CMB-derived parameter combination. BAO constrains this parameter more tightly than the CMB itself; the three SN compilations do not. In every extension of LCDM we consider, the leading measurable direction remains V_0, and it is where most of the tension with the CMB resides. In the w0-wa extension a second direction V_1 becomes measurable and provides an independent test of dynamical dark energy; the data show no significant tension in this direction. The only other beyond-LCDM extension that opens a genuinely new measurable direction is spatial curvature, and only marginally and only for BAO; both measurable directions then independently prefer positive spatial curvature, though the second direction is poorly constrained.

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.

Referee Report

2 major / 0 minor

Summary. The manuscript applies an SVD decomposition to low-redshift distance measurements from DESI BAO and three Type Ia supernova compilations. It identifies the leading direction V_0 (with amplitude c_0) as corresponding to high accuracy with a measurement of Ω_m h², reports that BAO constrains this combination more tightly than the CMB while the SN samples do not, and states that this direction captures most of the tension with CMB-anchored LCDM predictions; in extensions, V_0 remains the leading measurable direction except for w0-wa (where V_1 tests dynamical dark energy with no tension) and spatial curvature (where both directions marginally prefer positive curvature for BAO).

Significance. If the mapping of V_0 to Ω_m h² is robust, the work supplies a data-driven decomposition that localizes tensions to specific linear combinations and supplies independent tests of extensions, offering a clearer interpretation of what BAO and SN distance data actually measure beyond conventional parameter fits.

major comments (2)
  1. [Abstract] Abstract: the central claim that V_0 is 'to high accuracy' a measurement of Ω_m h² rests on an untested linearity assumption in the distance-redshift mapping; the manuscript provides no explicit check (finite-difference vs. analytic derivatives, mock recovery, or projection of second-order curvature/dark-energy terms) that higher-order contributions at the probed redshifts do not rotate V_0 or contaminate c_0 with w or Ω_k.
  2. [Abstract] Abstract: no information is given on data selection criteria, covariance matrix construction (including low-z systematics), robustness tests against fiducial cosmology choice, or error propagation through the SVD; these omissions are load-bearing for assessing whether the reported alignment with Ω_m h² and the relative constraining power of BAO vs. CMB hold.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that V_0 is 'to high accuracy' a measurement of Ω_m h² rests on an untested linearity assumption in the distance-redshift mapping; the manuscript provides no explicit check (finite-difference vs. analytic derivatives, mock recovery, or projection of second-order curvature/dark-energy terms) that higher-order contributions at the probed redshifts do not rotate V_0 or contaminate c_0 with w or Ω_k.

    Authors: We agree that an explicit validation of the linearity assumption would strengthen the central claim. In the revised manuscript we will add an appendix performing finite-difference checks on the distance-redshift relation at DESI and SN redshifts, comparing against analytic derivatives and projecting second-order contributions from w and Ω_k. This will quantify any rotation of V_0 or contamination of c_0 and confirm the alignment remains accurate to the stated level. revision: yes

  2. Referee: [Abstract] Abstract: no information is given on data selection criteria, covariance matrix construction (including low-z systematics), robustness tests against fiducial cosmology choice, or error propagation through the SVD; these omissions are load-bearing for assessing whether the reported alignment with Ω_m h² and the relative constraining power of BAO vs. CMB hold.

    Authors: The manuscript body describes the DESI BAO and three SN compilations employed, but we acknowledge the abstract and methods summary omit explicit details on selection criteria, covariance construction (including low-z systematics), fiducial-cosmology robustness, and SVD error propagation. We will revise the abstract to include a concise methods statement and expand the main text with a dedicated subsection covering these elements, including additional robustness tests. revision: yes

Circularity Check

0 steps flagged

No circularity: SVD applied to external data yields directions interpreted via model comparison

full rationale

The paper performs an SVD decomposition directly on the covariance or response of external low-redshift distance data from DESI BAO and SN compilations. The leading vector V_0 and its amplitude c_0 are extracted from the data; the subsequent claim that this direction measures Omega_m h^2 is presented as an empirical finding obtained by projecting the data onto the data-derived mode and comparing the result to the parameter dependence in cosmological models. No step reduces a fitted quantity to a prediction by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The derivation therefore remains self-contained against the supplied observational inputs and standard linear-algebra operations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of applying SVD to isolate physical parameter directions from the distance data; the abstract invokes no new entities and minimal free parameters beyond the measured amplitudes.

axioms (1)
  • domain assumption Low-redshift distance measurements admit an accurate linear SVD decomposition whose leading modes map directly to CMB-derived parameter combinations such as Omega_m h^2.
    This premise is required to conclude that V0 measures Omega_m h^2 and to localize tensions.

pith-pipeline@v0.9.1-grok · 5735 in / 1323 out tokens · 77916 ms · 2026-06-30T04:38:15.253414+00:00 · methodology

discussion (0)

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