Extended fast action minimization method: Application to SDSS-DR12 combined sample

We present the first application of the extended Fast Action Minimization method (eFAM) to a real data set, 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=1090pm 29(Mpc)-1, and H(z=0.38)r s/r fid s=83pm 3(km s-1 Mpc-1), in agreement with previous measurements on the same data set. 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-1Mpc, i.e. well into the non-linear regime. Besides, eFAM successfully removes the anisotropies due to redshift-space distortion (RSD) 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 α and απ of about 40 per cent and that on the non-linear damping scale ςπ of about 70 per cent. 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.