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We present a Bayesian phase-space reconstruction of the cosmic large-scalematter density and velocity fields from the SDSS-III Baryon OscillationsSpectroscopic Survey Data Release 12 (BOSS DR12) CMASS galaxy clusteringcatalogue. We rely on a given $\Lambda$CDM cosmology, a mesh resolution in therange of 6-10 $h^{-1}$ Mpc, and a lognormal-Poisson model with a redshiftdependent nonlinear bias. The bias parameters are derived from the data and ageneral renormalised perturbation theory approach. We use combined Gibbs andHamiltonian sampling, implemented in the \textsc{argo} code, to iterativelyreconstruct the dark matter density field and the coherent peculiar velocitiesof individual galaxies, correcting hereby for coherent redshift spacedistortions (RSD). Our tests relying on accurate $N$-body based mock galaxycatalogues, show unbiased real space power spectra of the nonlinear densityfield up to $k\sim0.2\, h$ Mpc$^{-1}$, and vanishing quadrupoles down to$r\sim20\,h^{-1}$ Mpc. We also demonstrate that the nonlinear cosmic web can beobtained from the tidal field tensor based on the Gaussian component of thereconstructed density field. We find that the reconstructed velocities have astatistical correlation coefficient compared to the true velocities of eachindividual lightcone mock galaxy of $r\sim0.68$ including about 10% ofsatellite galaxies with virial motions (about $r=0.75$ without satellites). Thepower spectra of the velocity divergence agree well with theoreticalpredictions up to $k\sim0.2\,h\,{\rm Mpc}^{-1}$. This work will be especiallyuseful to improve, e.g. BAO reconstructions, kinematic Sunyaev-Zeldovich (kSZ),integrated Sachs-Wolfe (ISW) measurements, or environmental studies.

The Clustering of Galaxies in the Completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmic Flows and Cosmic Web from Luminous Red Galaxies