Prepared for submission to JCAP Past and present cosmic structure in

Abstract. We present a chrono-cosmography project, aiming at the inference of the four dimen-sional 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 observa-tions, 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 fur-ther 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 dy-namic 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 th