Standard analyses of baryon acoustic oscillations (BAO) extract compressed scale parameters from galaxy clustering and interpret them using the sound horizon computed as an integral over the sound speed, rdintr_d^{\rm int}. Asensio-Rivera, Schöneberg, Gil-Marín and Verde (JCAP 07 (2026) 046) showed that the scale effectively imprinted in clustered matter and recovered by the estimators, rdobsr_d^{\rm obs}, differs from rdintr_d^{\rm int}, inducing a systematic bias in cosmological parameters that becomes a significant fraction of the statistical uncertainty for deviations of order ∣ΔΩm∣∼0.03|\Delta\Omega_m|\sim 0.03 and ∣ΔNeff∣∼0.3|\Delta N_{\rm eff}|\sim 0.3 at forecast DESI Year-5 (Stage-IV) precision, and proposed corrections (per-parameter-point bias computation, importance sampling, and a second-order Taylor expansion) that remove 90–96% or more of the systematic in the regimes explored. Their analysis, however, omitted BAO reconstruction, used a simplified Gaussian cubic-volume covariance, and excluded catalogue-level observational systematics. The open problem is to establish, at catalogue level and with full survey realism, whether this estimator–integral mismatch and the bias it induces persist at Stage-IV precision, and to deliver corrections validated to be sufficient across survey specifications, tracer samples, multi-probe likelihoods, and analysis choices, so that Stage-IV BAO analyses can either apply the corrections or assign a defensible systematic error budget.

Background

Baryon acoustic oscillations (BAO) are the relic imprint of sound waves that propagated through the photon–baryon plasma before recombination, appearing today as a preferred clustering scale of galaxies. The comoving distance sound waves travelled before baryons were released from photons at the drag epoch zd≈1060z_d\approx 1060 is the sound horizon, rdr_d, computed in standard analyses as the integral rdint=∫zd∞cs(z)/H(z) dzr_d^{\rm int}=\int_{z_d}^{\infty}c_s(z)/H(z)\,dz of the sound speed over the expansion history. Because rdr_d can be calculated precisely within a given cosmological model, it serves as a 'standard ruler': measuring the apparent BAO scale in galaxy redshift surveys yields relative distance constraints. Template-based BAO analyses compress the measurement into dilation parameters — the isotropic αiso\alpha_{\rm iso} and the anisotropic Alcock–Paczynski parameter αAP\alpha_{\rm AP} (the anisotropic distortion arising because a fiducial cosmology must be assumed to convert observed redshifts and angles into comoving separations) — by fitting a template power spectrum or correlation function from the fiducial cosmology to the data while marginalizing over nuisance parameters. The interpretation step then translates these into cosmological parameters using rdintr_d^{\rm int} from a Boltzmann code. The subtlety is that the scale actually imprinted in the clustered matter and extracted by this procedure, rdobsr_d^{\rm obs}, is not exactly the integral: non-linear evolution, Silk damping (the pre-recombination erasure of small-scale photon–baryon fluctuations), and the extraction machinery itself — de-wiggling algorithms that separate the oscillatory BAO component from the smooth broadband power spectrum, broadband nuisance marginalization, and effective-field-theory counterterms (higher-derivative correction terms of perturbative large-scale-structure modeling) — all shift it. The mismatch rdint≢rdobsr_d^{\rm int}\not\equiv r_d^{\rm obs} partially cancels when inference is done relative to a fiducial cosmology treated the same way, but not exactly. Thepsuriya and Lewis (JCAP 01 (2015) 034) first quantified this inaccuracy for then-current surveys; Carter, Beutler, Percival, DeRose, Wechsler and Zhao (MNRAS 494 (2020) 2076) extended the study with simulations including BAO reconstruction — the standard technique that sharpens the BAO feature by reversibly undoing large-scale bulk flows — finding the effect subdominant at BOSS-era precision. Asensio-Rivera et al. (JCAP 07 (2026) 046) generalized the analysis to a broad class of beyond-Λ\LambdaCDM cosmologies (varying Ωm\Omega_m, NeffN_{\rm eff} — the effective number of relativistic species — the recombination history, and pre-recombination dark energy) and to surveys with DESI-like precision, finding the induced bias grows roughly linearly with the departure from the fiducial cosmology and becomes a significant fraction of the statistical error for ∣ΔΩm∣≈0.03|\Delta\Omega_m|\approx 0.03–0.050.05 or ∣ΔNeff∣≈0.3|\Delta N_{\rm eff}|\approx 0.3–0.40.4 at forecast DESI Year-5 precision. Following a widely used convention, they treat the bias as significant when it reaches one-fifth of the statistical uncertainty (e.g. Δα=σα/5\Delta\alpha=\sigma_\alpha/5). They proposed corrections — computing the bias at each point of an MCMC (Markov-chain Monte Carlo) exploration, importance-sampling the posterior with the correction, or applying a second-order Taylor expansion of the bias in {Ωb+cdmh2,Neff,Ωbh2}\{\Omega_{b+{\rm cdm}}h^2, N_{\rm eff}, \Omega_b h^2\} — verified to reduce the systematic by at least 90% (typically 96% or more) within the parameter ranges explored. However, their pipeline neglected reconstruction, used a Gaussian cubic-volume covariance rather than the survey mask and full covariance, and excluded catalogue-level systematics, deferring to Carter et al. (2020) for the argument that these simplifications do not qualitatively invalidate the findings. DESI (Dark Energy Spectroscopic Instrument) and Euclid are Stage-IV spectroscopic galaxy surveys whose BAO scale measurements reach roughly 0.1% precision — the regime in which this systematic matters; the official DESI DR2 BAO analysis (Phys. Rev. D 112 (2025) 083515) does not yet include this effect in its systematic error budget.

Problem Statement

Establish whether the sound-horizon estimator–integral mismatch (rdint≢rdobsr_d^{\rm int}\not\equiv r_d^{\rm obs}) and the cosmological-parameter bias it induces survive full analysis realism at Stage-IV survey precision, and deliver corrections demonstrated to be sufficient in that regime, so that BAO analyses from DESI Year-5, Euclid, and comparable surveys either apply the corrections or assign a defensible systematic error budget. Concretely, building on Asensio-Rivera et al. (JCAP 07 (2026) 046): (i) Catalogue-level validation — quantify the mismatch and the induced bias in mock galaxy catalogues processed with full survey realism, including BAO reconstruction, survey masking and realistic geometry, the full (non-Gaussian) covariance, and catalogue-level observational systematics, for cosmologies with early-universe modifications of the size that matter at Stage-IV precision (e.g. ∣ΔNeff∣∼0.3|\Delta N_{\rm eff}|\sim 0.3, ∣ΔΩm∣∼0.05|\Delta\Omega_m|\sim 0.05, and compensated variants — cosmologies in which parameter shifts combine to keep the BAO dilation parameters approximately unchanged over the survey redshift range, so that galaxy and quasar BAO data alone cannot exclude them). (ii) Correction fidelity — validate the proposed corrections (per-parameter-point bias computation, posterior importance sampling, and the second-order Taylor expansion of the bias) for other survey specifications, for different tracer combinations, and for multi-probe likelihoods, and quantify residual higher-order terms beyond the second-order expansion for larger multi-parameter excursions than those explored. (iii) Analysis-choice dependence — map how the mismatch and the corrections interplay with different de-wiggling algorithms and alternative broadband parametrizations and their priors. (iv) Practical embedding — demonstrate that the fast per-point bias computation or Taylor correction (or an emulator-based full-modeling alternative) can be embedded in a large-scale MCMC/likelihood pipeline at acceptable computational cost. These components jointly support one objective — unbiased Stage-IV BAO cosmological inference — and the completion boundary is a demonstration, requiring component (i) in all cases and components (ii)–(iv) whenever the bias is found non-negligible, at catalogue level and across the stated regimes, that the mismatch-induced bias is either negligible compared to the statistical errors, corrected to below them, or otherwise accounted for through a defensible systematic error budget, with significance judged by the convention that the bias becomes important when it reaches one-fifth of the statistical uncertainty.

References

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