The BAO scale -- how standard is the standard ruler?

Francisco Asensio-Rivera; H\'ector Gil-Mar\'in; Licia Verde; Nils Sch\"oneberg

REVIEW 3 major objections 3 minor 1 cited by

The BAO scale -- how standard is the standard ruler?

T0 review · 3 major / 3 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read BAO's standard ruler is not perfectly standard: computing the sound horizon by integral instead of the clustering-imprinted scale biases Ω_m by ~0.03 and N_eff by ~0.3 at DESI Y5 precision.

desk verdict Useful, transparent extension of a known BAO systematic to new models and DESI Y5; headline numbers have an internal inconsistency and the reconstruction caveat is real, but the work should be refereed. read the letter →

arxiv 2603.03443 v2 pith:V6POVU7X submitted 2026-03-03 astro-ph.CO

Francisco Asensio-Rivera , Nils Schöneberg , Héctor Gil-Marín , Licia Verde This is my paper · ORCID

classification astro-ph.CO

keywords baryonacousticoscillationsBAOshiftparametersoundhorizonstandardrulerfiducialcosmologydependenceDESIYear5forecasteffectivenumberofrelativisticspeciescompressedparameters

topics Dark Energy

open problems Dark Energy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

BAO cosmology assumes the 'standard ruler' — the sound horizon at baryon drag — can be computed by a one-line integral and used to interpret compressed BAO measurements. This paper argues the assumption is not exact: the scale actually imprinted in galaxy clustering is slightly different from the integral, and the difference shows up as a systematic bias when the fitted cosmology moves away from the fiducial one. At DESI Year-5 precision the bias becomes a significant fraction (about one fifth) of the statistical error once Ω_m is off by 0.03 or N_eff by 0.3. The bias survives a realistic non-linear pipeline and can be corrected with a cheap Taylor expansion, so the authors recommend corrections or a systematic budget for such explorations.

What carries the argument

The central object is the ratio s = r_d^fid / r_d for the cosmology being fitted, compared with the same ratio computed by the integral definition r_int. The BAO shift α — the measured size of the acoustic feature relative to a fiducial template — is what cosmology fits actually constrain, and any difference between the integral ratio and the 'observed' ratio propagates directly into α. The paper constructs four increasingly realistic extractions of the observed BAO scale (peak positions; de-wiggled BAO-only oscillations; a full power-spectrum template with broadband nuisance polynomials; and a correlation-function template), plus a DESI-like EFT pipeline with multipoles, and measures the bi

What would settle it

Run a DESI-Y5-like mock analysis that includes BAO reconstruction and a realistic survey window, and measure the recovered α shift for models at |ΔΩ_m| = 0.03 and |ΔN_eff| = 0.3; if the shift is much smaller or larger than the 1/5-σ level reported here, the thresholds and the need for correction change. Also compare the paper's second-order Taylor-expansion prediction for a three-parameter corner cosmology against a full template minimization; the paper reports a worst-case 8% residual, so any substantially larger residual would falsify the adequacy of that correction.

Watch

Extended reading notes

Core claim

The paper's central claim is that the scale conventionally read off BAO data is not the same as the scale defined by the textbook sound-horizon integral. For compressed BAO analyses — where the shift α is interpreted through the ratio r_d^fid / r_d — using the integral r_int in the interpretation step while the data extraction sees the actual oscillation scale r_obs creates a systematic mismatch. Quantifying this across a wider model space than earlier work (including pre-recombination physics, early dark energy, varying electron mass, massive neutrinos, and 'compensated' cosmologies), the authors find that for DESI Year-5 volume and noise the mismatch becomes a significant fraction of the s

Load-bearing premise

The load-bearing premise is that the simplified, reconstruction-free template fits used throughout the paper respond to cosmology the same way a full DESI BAO pipeline with reconstruction, masking, and realistic covariance does; the paper leans on an earlier simulation-based study for this, and if that transfer fails the quoted thresholds shift.

Editorial extensions

If this is right

For DESI Y5-like analyses that vary Ω_m or N_eff beyond about 0.03 or 0.3 from the fiducial, ignoring the mismatch adds a systematic comparable to 0.2σ or more; the paper recommends either correcting or inflating the error budget.
A second-order Taylor expansion in {Ω_cdm h², Ω_b h², N_eff} reproduces the bias to within roughly 10% of the statistical error in the worst tested two- or three-parameter cases, and typically much better.
The bias slopes are nearly independent of survey volume and noise, so a correction precomputed for a high-precision idealized survey can be applied to realistic surveys.
DESI Year-1 and smaller surveys are not significantly affected; the thresholds for Y1 are roughly three times larger.
The effect matters most in models that open degeneracies: compensated cosmologies that keep α_int = 1 by shifting N_eff and h in tandem still show >1σ bias for DESI Y5.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the bias scales with statistical precision, any survey that beats DESI Y5 errors will hit the 1/5-σ threshold for smaller parameter deviations; the effect is likely to become a standard component of BAO systematics budgets for future experiments.
A cleaner long-term fix suggested by the paper's own comparison is to stop using the integral in the interpretation step altogether and instead calibrate the effective BAO scale from the same template family used in the fit; the paper mentions this avoidance route but focuses on corrections because of computational cost.
The quoted thresholds are for deviations from the authors' adopted Planck-like ΛCDM fiducial; analyses using a different fiducial can reuse the same machinery, but the numerical threshold values would shift.
The reliance on an earlier simulation study for reconstruction means the DESI Y5 thresholds should be re-checked once real Y5 reconstruction is available; the direction of any change is unknown.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a solid, useful paper on a known but underappreciated systematic. The core mismatch between the integral sound horizon and the scale actually imprinted in clustering has been known since Thepsuriya & Lewis (2015) and Carter et al. (2020), but this paper extends it to pre-recombination dark energy, varying electron mass, and compensated Neff–h cosmologies, and quantifies the impact for DESI Y5-like surveys. The Taylor correction framework is a practical addition—the coefficients are transparently derived and checked on held-out corners.

What's good: the methodology is clear, the synthetic forecasts are documented, and the paper cross-checks against earlier work. The conclusions are stated carefully: for most parameters and for DESI Y1 the effect is negligible; it matters mainly for Omega_m and N_eff in extended models. The paper is honest about its simplifications.

Soft spots, in proportion. First, there is an internal inconsistency: the abstract and Sec. 3 quote |Delta Omega_m| ~ 0.03 and |Delta N_eff| ~ 0.3 as the thresholds for DESI Y5, while Sec. 6 says 0.05 and 0.4. That has to be reconciled. Second, the thresholds come from a simplified pipeline without reconstruction, masking, or the real covariance. The paper argues, following Carter et al., that these don't change the conclusions, and its own Sec. 4 check on two compensated cosmologies is reassuring. But the stress-test note is right that Carter et al. reported larger biases (0.4% vs 0.2% at |Delta N_eff| = 1). That goes in the direction of making the effect larger, not smaller, so it strengthens the paper's warning rather than undermining it, but it also means the exact thresholds should be treated as approximate. The Taylor coefficients are calibrated on the same synthetic data, though the held-out validation mitigates that. None of these is load-bearing; they affect the precise numbers, not the existence of the effect.

Who it's for: BAO analysts interpreting compressed alpha measurements, especially in extended models, and DESI Y5 teams doing systematics budgets. It deserves a serious referee. My recommendation: send it to peer review. It will need a revision to fix the inconsistency and soften the reconstruction claim, but the central argument holds up.

Referee Report

3 major / 3 minor

Summary. The paper studies whether the BAO scale extracted from galaxy clustering is identical to the integral sound horizon r_d^int used in standard compressed-parameter interpretations. It compares several estimators (r_peak, r_P(k) BAO, r_P(k) full, r_ξ) against r_d^int for variations in Ω_b h^2, Ω_m, N_eff, early-Universe recombination models, early dark energy, and massive neutrinos, using DESI-like survey volumes and a Gaussian covariance. The central claim is that the bias Δα/α becomes a significant fraction of the statistical uncertainty for deviations |ΔΩ_m|≈0.03 and |ΔN_eff|≈0.3 for DESI Y5. The paper also implements a more realistic non-linear, redshift-space pipeline and proposes mitigation strategies, including a second-order Taylor expansion in a reduced parameter set.

Significance. If the central claim holds, this is an important systematic for DESI Y5 and other Stage-IV surveys, particularly when fitting extended cosmological models that allow Ω_m or N_eff to drift far from the fiducial values. The paper's strengths are its deterministic, non-stochastic methodology; explicit cross-checks against Ref. [14]; an extended parameter space including pre-recombination physics; a non-linear RSD pipeline in Sec. 4; and concrete correction strategies. The claimed thresholds, however, are not yet the robust result they appear to be: they depend on the simplified likelihood and on an extrapolation about the effect of BAO reconstruction that is not demonstrated here.

major comments (3)

[Section 6 (Conclusions)] The thresholds quoted in the Conclusions, |ΔΩ_m|≈0.05 and |ΔN_eff|≈0.4, contradict the abstract and Secs. 3.3/3.4, which state |ΔΩ_m|=0.03 and |ΔN_eff|=0.3, and also Table 4, which gives 0.029/0.30 for DESI Y5 total. This is not a rounding difference and changes the practical guidance. Please reconcile the numbers and state the exact criterion (e.g., 1/5 σ_α) in one place.
[Sec. 4 and Conclusions] The quantitative thresholds are computed with a pipeline that omits BAO reconstruction, masking, and the real survey covariance. The claim that Ref. [32] shows these simplifications do not affect the findings is not supported by the comparison in App. A, where Ref. [32] finds ~0.4% bias at |ΔN_eff|=1 versus 0.2% here. Since the bias-vs-parameter surface is what sets the thresholds, please either run a reconstructed version of the Comp. 1/Comp. 2 test or provide an analytic argument that reconstruction affects only the amplitude/errors and not the cosmology dependence of the BAO scale.
[Sec. 5, Eq. (5.1)] The Taylor-expansion parameter set θ={Ω_b+cdm h^2, N_eff, Ω_b h^2} omits Σmν, but Table 4 gives a Y5-total allowed deviation of +0.482 eV, comparable to the headline thresholds and within the KATRIN bound. The proposed correction is therefore incomplete for a viable parameter direction. Include Σmν in the expansion or justify the omission explicitly.

minor comments (3)

[References] Refs. [18] and [32] are the same paper (Carter et al. 2020); please consolidate to avoid duplicate citation.
[Eq. (2.3) and text] 'Thompson scattering' should be 'Thomson scattering'; also in Eq. (2.7) there is a missing space in 'noiseN in'.
[Fig. 1 and Sec. 2.2] Consider labeling the x-axis consistently as h Mpc^-1 and noting the unit convention in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bias is measured from independent BAO extraction routes on the same synthetic spectra, and the central thresholds are not fitted parameters.

full rationale

The paper's central claim is that the sound horizon derived from the integral r_int^d differs from the effective scale imprinted in the power spectrum or correlation function, and that this mismatch biases BAO shift parameters for cosmologies sufficiently far from the fiducial model. This is established by computing r_int^d from equation (2.1) and independently extracting the BAO scale using four distinct template/peak methods applied to the same synthetic power spectra and correlation functions; no free parameter is adjusted to force the observed Δα/α. The quoted thresholds (|ΔΩ_m|≈0.03, |ΔN_eff|≈0.3 for DESI Y5) are derived by comparing the measured bias to forecast statistical uncertainties, not from fitting the threshold itself. The Taylor-expansion correction in Section 5 is indeed a fit to the calculated bias surface, but it is explicitly validated on held-out multi-parameter corners in Appendix E and is presented as a calibration/emulator rather than as the derivation of the effect. Self-citations appear (e.g., de-wiggling method [22], thesis [23], compensated-cosmology inputs [54]), but none is load-bearing for the main result: the full-model and correlation-function routes do not rely on the de-wiggling method, and [32] is an external study used only for a robustness caveat about reconstruction. The paper is self-contained in its quantitative comparison and does not reduce to defining its output in terms of its inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim does not introduce new physical entities. It relies on standard cosmological perturbation theory, simulation-based mocks, and a set of calibration parameters for the correction formula. The most important free/ad hoc inputs are the survey specifications, the 1/5-σ threshold, and the fitted Taylor coefficients.

free parameters (4)

Taylor correction Jacobian/Hessian coefficients = ∂b/∂x=-0.0398, ∂b/∂y=0.341, ∂b/∂z=-0.00145; Hessian in Eq. 5.4
Coefficients of the quadratic bias model in Sec. 5 are computed from the same synthetic grid that defines the bias; they are calibration constants, not derived independently.
DESI-like survey volume and shot noise = Y5 total: V=30 Gpc^3/h^3, N=3100 Mpc^3/h^3; Y1 total: V=5.4 Gpc^3/h^3, N=5500 Mpc^3/h^3
Table 1 specifications approximate the real surveys by hand; thresholds scale with these numbers.
Significance threshold = 1/5
The 'significant bias' criterion of 1/5 of the statistical uncertainty is adopted from [39]; results would change with a different criterion.
PCS finesse Δ = not specified
Controls broadband marginalization in Eq. 2.17; authors note it is 'of paramount importance' but do not give the adopted value.

assumptions (5)

domain assumption BAO template methods recover the true BAO scale up to the modeled effects, and broadband terms can be marginalized without absorbing the BAO signal.
Central to all estimators in Sec. 2; the PCS finesse discussion in Sec. 2.4 explicitly assumes the nuisance spline does not eat the BAO wiggle.
domain assumption A Gaussian covariance with effective volume and shot noise approximates DESI survey errors.
Used in Eqs. (2.7)-(2.8) and the survey specifications in Table 1; no survey window or realistic covariance is included.
domain assumption The conclusion of [32] that reconstruction does not change the fiducial-cosmology BAO bias transfers to this setup.
Invoked in Sec. 4 and the Conclusions to justify omitting reconstruction; not tested in this paper.
domain assumption Linear theory plus one-loop EFT (velocileptors) describes the nonlinear matter/galaxy power spectrum at k≤0.3 h/Mpc without additional shifts.
Basis for the DESI-like mock data vectors in Sec. 2.4.
domain assumption Initial conditions are adiabatic.
Stated in Sec. 2.1; isocurvature or non-adiabatic modes are not considered.

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Cite this review

Pith. "Pith review of The BAO scale -- how standard is the standard ruler?." pith.science (2026). https://pith.science/paper/V6POVU7X

@misc{pith2026260303443,
  author       = {Pith},
  title        = {Pith review of: The BAO scale -- how standard is the standard ruler?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V6POVU7X}},
  note         = {Machine review of arXiv:2603.03443}
}

abstract

Analyses of baryon acoustic oscillations (BAO) commonly employ template-based methods to extract compressed parameters from the clustering of dark-matter tracers, which are then interpreted in terms of ratios of the sound-horizon scale and cosmological distances relative to a fiducial cosmology. A small mismatch between the sound-horizon scale derived from the standard analytic formulation (integral over the sound speed) and the effective scale imprinted in clustered matter can, however, introduce a systematic bias in cosmological inference. We extend previous work to a broader class of cosmological models, quantify this bias for surveys with DESI-like precision, and propose strategies to correct for the effect. We find that the induced bias becomes a significant fraction of the statistical uncertainty for deviations from the fiducial cosmology, at the level of $|\Delta \Omega_m| = 0.03$ and $|\Delta N_\mathrm{eff}| = 0.3$, and for very precise data corresponding to a forecasted Year-5 DESI survey (or other stage IV dark energy galaxy surveys). We present several ways to correct for this effect, suitable for a variety of applications. We therefore recommend that analyses exploring such parameter regimes either apply the proposed corrections or include an appropriate systematic error budget.

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