  We present a self-consistent Bayesian formalism to sample the primordial
density fields compatible with a set of dark matter density tracers after
cosmic evolution observed in redshift space. Previous works on density
reconstruction did not self-consistently consider redshift space distortions or
included an additional iterative distortion correction step. We present here
the analytic solution of coherent flows within a Hamiltonian Monte Carlo
posterior sampling of the primordial density field. We test our method within
the Zel'dovich approximation, presenting also an analytic solution including
tidal fields and spherical collapse on small scales using augmented Lagrangian
perturbation theory. Our resulting reconstructed fields are isotropic and their
power spectra are unbiased compared to the true one defined by our mock
observations. Novel algorithmic implementations are introduced regarding the
mass assignment kernels when defining the dark matter density field and
optimization of the time step in the Hamiltonian equations of motions. Our
algorithm, dubbed barcode, promises to be specially suited for analysis of the
dark matter cosmic web down to scales of a few Megaparsecs. This large scale
structure is implied by the observed spatial distribution of galaxy clusters
--- such as obtained from X-ray, SZ or weak lensing surveys --- as well as that
of the intergalactic medium sampled by the Lyman alpha forest or perhaps even
by deep hydrogen intensity mapping. In these cases, virialized motions are
negligible, and the tracers cannot be modeled as point-like objects. It could
be used in all of these contexts as a baryon acoustic oscillation
reconstruction algorithm.
