Extended Fast Action Minimisation method: application to SDSS-DR12
  Combined Sample
  We present the first application of the extended Fast Action Minimization
method (eFAM) to a real dataset, the SDSS-DR12 Combined Sample, to reconstruct
galaxies orbits back-in-time, their two-point correlation function (2PCF) in
real-space, and enhance the baryon acoustic oscillation (BAO) peak. For this
purpose, we introduce a new implementation of eFAM that accounts for selection
effects, survey footprint, and galaxy bias. We use the reconstructed BAO peak
to measure the angular diameter distance, D_A(z)r^{fid}_s/r_s, and the Hubble
parameter, H(z)r_s/r^{fid}_s, normalized to the sound horizon scale for a
fiducial cosmology r^{fid}_s, at the mean redshift of the sample z=0.38,
obtaining D_A(z=0.38)r^{fid}_s/r_s=1090 +/- 29 (Mpc)^{-1}, and
H(z=0.38)r_s}/r^{fid}_s=83 +/- 3 (km s^{-1}Mpc^{-1}), in agreement with
previous measurements on the same dataset. The validation tests, performed
using 400 publicly available SDSS-DR12 mock catalogues, reveal that eFAM
performs well in reconstructing the 2PCF down to separations of 25h^{-1}Mpc$,
i.e. well into the non-linear regime. Besides, eFAM successfully removes the
anisotropies due to redshift-space distortion at all redshifts including that
of the survey, allowing us to decrease the number of free parameters in the
model and fit the full-shape of the back-in-time reconstructed 2PCF well beyond
the BAO peak. Recovering the real-space 2PCF, eFAM improves the precision on
the estimates of the fitting parameters. When compared with the
no-reconstruction case, eFAM reduces the uncertainty of the Alcock-Paczynski
distortion parameters of about 40% and that on the non-linear damping scale of
about 70%. These results show that eFAM can be successfully applied to existing
redshift galaxy catalogues and should be considered as a reconstruction tool
for next-generation surveys alternative to popular methods based on the
Zel'dovich approximation.
