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

The method of constrained realization (CR) of Gaussian random fields is applied here to reconstruct our ''local'' universe. A large observational data set is sampled and used as constraints imposed on realizations of an assumed primordial Gaussian perturbation field. To illustrate the method, the velocity potential as obtained by the POTENT algorithm from the observed velocity field is sampled at 181 different positions within a sphere of 40 h-1 Mpc radius around us. Numerical realizations of the standard cold dark matter (CDM) model are constructed to yield the actual sampled values. These realizations do reconstruct the density perturbation field of the nearby universe. With only 181 constraints, the CR algorithm recovers the main features of POTENT's density 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 method is easily applicable to the general case where any variable which depends linearly on the Gaussian field can be used to set the constraints. In the cosmological case these realizations are used to set initial conditions for numerical simulations.