One of the great challenges of the coming years is to rigorously test these theories using observations (Werner et al. 2014) and disentangle the interplay between dark matter and dark energy (Park & Lee 2007 Bos et al. Therefore, the cosmic web encodes the information to understand non-linear structure formation (Bond, Kofman & Pogosyan 1996 van de Weygaert 1996 Alpaslan et al. At initial cosmic times, perturbations are linear and the statistics describing them is extremely close to Gaussian, though some deviations from Gaussianity could be expected depending on the inflationary phase the Universe has probably experienced after its birth (Starobinsky 1980 Planck Collaboration X 2018a). The cosmic web of the Universe arises from the gravitational instability caused by tiny primordial density perturbations, which presumably have their origin in quantum fluctuations. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm. In these cases, virialized motions are negligible, and the tracers cannot be modelled as point-like objects. This large-scale structure is implied by the observed spatial distribution of galaxy clusters – such as obtained from X-ray, Sunyaev–Zel’dovich, or weak lensing surveys – as well as that of the intergalactic medium sampled by the Ly α forest or perhaps even by deep hydrogen intensity mapping. Our algorithm, dubbed barcode, promises to be specially suited for analysis of the dark matter cosmic web down to scales of a few megaparsecs. 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 resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true field defined by our mock observations. We test our method within the Zel’dovich approximation, presenting also an analytic solution including tidal fields and spherical collapse on small scales. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after a cosmic evolution observed in redshift space.
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