The Initial Conditions of the Universe from Constrained Simulations (1203.4184v2)

Abstract: I present a new approach to recover the primordial density fluctuations and the cosmic web structure underlying a galaxy distribution. The method is based on sampling Gaussian fields which are compatible with a galaxy distribution and a structure formation model. This is achieved by splitting the inversion problem into two Gibbs-sampling steps: the first being a Gaussianisation step transforming a distribution of point sources at Lagrangian positions -which are not a priori given- into a linear alias-free Gaussian field. This step is based on Hamiltonian sampling with a Gaussian-Poisson model. The second step consists on a likelihood comparison in which the set of matter tracers at the initial conditions is constrained on the galaxy distribution and the assumed structure formation model. For computational reasons second order Lagrangian Perturbation Theory is used. However, the presented approach is flexible to adopt any structure formation model. A semi-analytic halo-model based galaxy mock catalog is taken to demonstrate that the recovered initial conditions are closely unbiased with respect to the actual ones from the corresponding N-body simulation down to scales of a ~ 5 Mpc/h. The cross-correlation between them shows a substantial gain of information, being at k ~ 0.3 h/Mpc more than doubled. In addition the initial conditions are extremely well Gaussian distributed and the power-spectra follow the shape of the linear power-spectrum being very close to the actual one from the simulation down to scales of k ~ 1 h/Mpc.