We present a chrono-cosmography project, aiming at the inference of the four
dimensional formation history of the observed large scale structure from its
origin to the present epoch. To do so, we perform a full-scale Bayesian
analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS)
Data Release 7 main galaxy sample, relying on a fully probabilistic, physical
model of the non-linearly evolved density field. Besides inferring initial
conditions from observations, our methodology naturally and accurately
reconstructs non-linear features at the present epoch, such as walls and
filaments, corresponding to high-order correlation functions generated by
late-time structure formation. Our inference framework self-consistently
accounts for typical observational systematic and statistical uncertainties
such as noise, survey geometry and selection effects. We further account for
luminosity dependent galaxy biases and automatic noise calibration within a
fully Bayesian approach. As a result, this analysis provides highly-detailed
and accurate reconstructions of the present density field on scales larger than
∼3 Mpc/h, constrained by SDSS observations. This approach also leads to
the first quantitative inference of plausible formation histories of the
dynamic large scale structure underlying the observed galaxy distribution. The
results described in this work constitute the first full Bayesian non-linear
analysis of the cosmic large scale structure with the demonstrated capability
of uncertainty quantification. Some of these results will be made publicly
available along with this work. The level of detail of inferred results and the
high degree of control on observational uncertainties pave the path towards
high precision chrono-cosmography, the subject of simultaneously studying the
dynamics and the morphology of the inhomogeneous Universe.Comment: 27 pages, 9 figure