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.
