Bayesian large-scale structure inference and cosmic web analysis
  Surveys of the cosmic large-scale structure carry opportunities for building
and testing cosmological theories about the origin and evolution of the
Universe. This endeavor requires appropriate data assimilation tools, for
establishing the contact between survey catalogs and models of structure
formation. In this thesis, we present an innovative statistical approach for
the ab initio simultaneous analysis of the formation history and morphology of
the cosmic web: the BORG algorithm infers the primordial density fluctuations
and produces physical reconstructions of the dark matter distribution that
underlies observed galaxies, by assimilating the survey data into a
cosmological structure formation model. The method, based on Bayesian
probability theory, provides accurate means of uncertainty quantification. We
demonstrate the application of BORG to the Sloan Digital Sky Survey data and
describe the primordial and late-time large-scale structure in the observed
volume. We show how the approach has led to the first quantitative inference of
the cosmological initial conditions and of the formation history of the
observed structures. We then use these results for several cosmographic
projects aiming at analyzing and classifying the large-scale structure. In
particular, we build an enhanced catalog of cosmic voids probed at the level of
the dark matter distribution, deeper than with the galaxies. We present
detailed probabilistic maps of the dynamic cosmic web, and offer a general
solution to the problem of classifying structures in the presence of
uncertainty. The results described in this thesis constitute accurate
chrono-cosmography of the inhomogeneous cosmic structure.
