CONSTRAINED REALIZATIONS OF GAUSSIAN FIELDS - RECONSTRUCTION OF THE LARGE-SCALE STRUCTURE

The method of constrained realization (CR) of Gaussian random fields i s applied here to reconstruct our ''local'' universe. A large observat ional data set is sampled and used as constraints imposed on realizati ons of an assumed primordial Gaussian perturbation field. To illustrat e the method, the velocity potential as obtained by the POTENT algorit hm from the observed velocity field is sampled at 181 different positi ons within a sphere of 40 h-1 Mpc radius around us. Numerical realizat ions of the standard cold dark matter (CDM) model are constructed to y ield the actual sampled values. These realizations do reconstruct the density perturbation field of the nearby universe. With only 181 const raints, the CR algorithm recovers the main features of POTENT's densit y field and, in particular, the Great Attractor region. The 12 h-1 Mpc smoothed potential, which depends on the very long wavelengths of the underlying perturbation field, is used to constrain high-resolution ( 5 h-1 Mpc smoothing) realizations. Thus, given an assumed model, high- resolution fields are created subject to low-resolution data. The meth od is easily applicable to the general case where any variable which d epends linearly on the Gaussian field can be used to set the constrain ts. In the cosmological case these realizations are used to set initia l conditions for numerical simulations.