BAO reconstruction: a swift numerical action method for massive spectroscopic surveys

A new fully non-linear reconstruction algorithm for the accurate recovery of the Baryonic Acoustic Oscillations (BAO) scale in two-point correlation functions is proposed, based on the least-action principle and extending the Fast Action Minimisation method by Nusser & Branchini (2000). Especially designed for massive spectroscopic surveys, it is tested on dark-matter halo catalogues extracted from the DEUS-FUR $\Lambda$CDM simulation to trace the trajectories of up to $\sim207,000$ haloes backward-in-time, well beyond the first-order Lagrangian approximation. The new algorithm successfully recovers the BAO feature in real and redshift-space in both the monopole and the anisotropic two-point correlation function, also for anomalous samples showing misplaced or absent signature of BAO. In redshift-space the non-linear displacement parameter $\Sigma_\mathrm{NL}$ is reduced from $11.8\pm0.3h^{-1}$Mpc at redshift $z=0$ (pre-reconstruction) to $4.0\pm0.5h^{-1}$Mpc at $z\simeq37$ after reconstruction. A comparison with the first-order Lagrangian reconstruction is presented, showing that this techniques outperforms the linear approximation in recovering an unbiased measurement of the acoustic scale.