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We present the first application of the extended Fast Action Minimizationmethod (eFAM) to a real dataset, the SDSS-DR12 Combined Sample, to reconstructgalaxies orbits back-in-time, their two-point correlation function (2PCF) inreal-space, and enhance the baryon acoustic oscillation (BAO) peak. For thispurpose, we introduce a new implementation of eFAM that accounts for selectioneffects, survey footprint, and galaxy bias. We use the reconstructed BAO peakto measure the angular diameter distance, D_A(z)r^{fid}_s/r_s, and the Hubbleparameter, H(z)r_s/r^{fid}_s, normalized to the sound horizon scale for afiducial 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}, andH(z=0.38)r_s}/r^{fid}_s=83 +/- 3 (km s^{-1}Mpc^{-1}), in agreement withprevious measurements on the same dataset. The validation tests, performedusing 400 publicly available SDSS-DR12 mock catalogues, reveal that eFAMperforms well in reconstructing the 2PCF down to separations of 25h^{-1}Mpc$,i.e. well into the non-linear regime. Besides, eFAM successfully removes theanisotropies due to redshift-space distortion at all redshifts including thatof the survey, allowing us to decrease the number of free parameters in themodel and fit the full-shape of the back-in-time reconstructed 2PCF well beyondthe BAO peak. Recovering the real-space 2PCF, eFAM improves the precision onthe estimates of the fitting parameters. When compared with theno-reconstruction case, eFAM reduces the uncertainty of the Alcock-Paczynskidistortion parameters of about 40% and that on the non-linear damping scale ofabout 70%. These results show that eFAM can be successfully applied to existingredshift galaxy catalogues and should be considered as a reconstruction toolfor next-generation surveys alternative to popular methods based on theZel'dovich approximation.

Extended Fast Action Minimisation method: application to SDSS-DR12 Combined Sample