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 cold dark matter simulation (Reverdy et al. 2015) to trace the trajectories of up to similar to 207000 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(NL) is reduced from 11.8 +/- 0.3 h(-1) Mpc at redshift z = 0 to 4.0 +/- 0.5 h(-1) Mpc at z similar or equal to 37 after reconstruction. A comparison with the first-order Lagrangian reconstruction is presented, showing that these techniques outperform the linear approximation in recovering an unbiased measurement of the acoustic scale.