Bayesian physical reconstruction of initial conditions from large scale structure surveys

We present a fully probabilistic, physical model of the non-linearly evolved density field, as probed by realistic galaxy surveys. Our model is valid in the linear and mildly non-linear regimes and uses second order Lagrangian perturbation theory to connect the initial conditions with the final density field. Our parameter space consists of the 3D initial density field and our method allows a fully Bayesian exploration of the sets of initial conditions that are consistent with the galaxy distribution sampling the final density field. A natural byproduct of this technique is an optimal non-linear reconstruction of the present density and velocity fields, including a full propagation of the observational uncertainties. A test of these methods on simulated data mimicking the survey mask, selection function and galaxy number of the SDSS DR7 main sample shows that this physical model gives accurate reconstructions of the underlying present-day density and velocity fields on scales larger than ~6 Mpc/h. Our method naturally and accurately reconstructs non-linear features corresponding to three-point and higher order correlation functions such as walls and filaments. Simple tests of the reconstructed initial conditions show statistical consistency with the Gaussian simulation inputs. Our test demonstrates that statistical approaches based on physical models of the large scale structure distribution are now becoming feasible for realistic current and future surveys.