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

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 $|ΔΩ_m| = 0.03$ and $|ΔN_\mathrm{eff}| = 0.3$, 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.

Figures (13)

• Figure 1: Analysis of the BAO frequency as a function of the scale for a cosmology with $\Omega_m=0.3$, $\Omega_b=0.05$, and $h=0.68$ ($r_d^\mathrm{int} = 147.46$Mpc). We compute the linear power spectrum using classclass and recover the oscillations using the de-wiggling method presented in Ghaemi:2025lgu ("Cubic Inflections"). Then, we use a Short-Time-Fourier-Transform from the tftb package (https://github.com/scikit-signal/tftb) to compute the instantaneous frequencies. We also show a comparison to the expected oscillation frequency $\omega=r_d^{\rm int}$ from \ref{['eq:rd_int']}. Modified version of Schoneberg:2021uak. The visible steps in the graph represent the bin/window size of the Short-Time-Fourier-Transform.
• Figure 2: Correlation function for the same cosmology as in \ref{['fig:rd_int_vs_stft']}. We show in a black dashed line the value of $r_d^\mathrm{int} = 147.46$ Mpc, while the purple marker shows the peak of the correlation function, and the green marker shows the peak of the correlation function once the broadband has been subtracted. The peak of the correlation function is at $148.93$ Mpc (+1%) without broadband subtraction and at $150.08$ Mpc (+1.8%) with broadband subtraction (using the same polynomial broadband of \ref{['eq:cf_template']}).
• Figure 3: Relative bias on $\alpha$ for the various methods of \ref{['sec:methods']} as a function of the amplitude $A_s$ with the vertical line indicating the fiducial value; the errors are forecasts for the DESI Y5 (total) survey specification. Left: Without the BAO amplitude as a nuisance parameter. Right: with a nuisance parameter for the BAO only method. Points are slightly offset horizontally for clarity.
• Figure 4: Dependence of the various ways of obtaining $s$ of \ref{['sec:methods']} on $\Omega_b h^2$ (left) and resulting $\Delta \alpha/\alpha$ relative to the one obtained from the integral definition of $r_d$ (right). Points are slightly offset horizontally for clarity. On the right panel, the horizontal green bands denote the region where the systematic shift in $\alpha$ is below 1/5 of the statistical error. The gray vertical band encloses the range of the cosmological parameter that satisfies this condition.
• Figure 5: Same as \ref{['fig:omegab']} but for the matter fractional abundance $\Omega_m$.