Gaussian fields and constrained simulations of the large-scale structure

Abstract

The formalism of the Wiener filter (WF) and constrained realizations (CRs) is reviewed here within the cosmological context of the primordial perturbations constituting a random Gaussian field. It is shown that in such a context the WF/CRs methodology is the optimal tool of reconstructing the (linear) large-scale structure of the universe from noisy, sparse and incomplete data. The emphasis of the chapter is on reviewing the WF and CR algorithm as applied to the linear regime of the gravitational instability and Gaussian random fields. Applications to the reconstruction of the cosmography from redshift and peculiar surveys are briefly reviewed. The main application reviewed here is that of constrained simulations (CSs), namely cosmological simulations in which the initial conditions are Gaussian random fields constrained by actual observational data. CSs of the 'local' universe reproduce, by construction, the large-scale features that are imposed by the observational data. They provide a platform for simulating the small-scale structure and galaxy formation in the 'local' universe within the actual observed large scales. One of the main virtues of the CSs is the reduction o the cosmic variance in simulations aimed at reproducing the observed 'local' universe and thereby improving and making tighter comparison between simulations and observations. © 2008 Springer-Verlag Berlin Heidelberg.