\textit{Euclid} preparation. Baryon acoustic oscillations extraction techniques: comparison and optimisation

TL;DR

This paper validates and optimizes the Euclid BAO analysis pipeline, demonstrating its accuracy, efficiency, and robustness in extracting cosmological parameters from mock data.

Contribution

It introduces methodological advances including an emulator-based model evaluator, a semi-analytical covariance estimator, and compares two BAO reconstruction methods, ensuring scalable and reliable analysis.

Findings

Both reconstruction methods produce unbiased BAO measurements across redshifts.

Reconstruction improves the figure of merit for key parameters by a factor of three.

BAO-only constraints reach approximately 10% on  and 3% on H_0 r_s.

Abstract

We present the first end-to-end validation of the Euclid baryon acoustic oscillation (BAO) analysis pipeline, encompassing density-field reconstruction, two-point correlation function measurement, and cosmological-parameter inference. Using eight Euclid-like mock catalogues from each of four Flagship I snapshots, designed to reproduce the expected statistical properties of the first Euclid data release (DR1), we assess the two standard BAO reconstruction methods based on the Zel'dovich approximation, RecSym and RecIso, across $0.9 \leq z \leq 1.8$. The pipeline introduces several methodological advances: an emulator-based model evaluator (Bora.jl) combined with a Hamiltonian Monte Carlo sampler (NUTS), achieving more than a 500-fold speed-up relative to standard Markov chain Monte Carlo, and a semi-analytical covariance estimator (BeXiCov+WinCov) that enables robust error estimates from only eight mock realisations while remaining stable under fiducial-cosmology variations. These components ensure computational efficiency while reducing the risk of underestimating parameter uncertainties. Both reconstruction schemes yield unbiased BAO measurements across all redshifts and analysis choices, including smoothing scale and fiducial cosmology. In each snapshot, reconstruction enhances the figure of merit for $\{\Omega_m, H_0 r_s\}$ by $\sim3$, equivalent to tripling the effective survey volume. Combining the four redshift bins, the improvement remains substantial, with BAO-only constraints reaching $\sim10\%$ precision on $\Omega_m$ and $\sim3\%$ on $H_0 r_s$. Results from RecSym and RecIso are consistent within uncertainties, though we recommend RecSym during testing due to its lower sensitivity to covariance variations. These findings establish the accuracy, robustness, and scalability of the Euclid BAO pipeline for DR1, providing a solid foundation for future cosmological analyses.