TRACING LARGE-SCALE FLUCTUATIONS BACK IN TIME

We present and test a quasi-linear method for recovering the growing mode of the initial fluctuations of a cosmological gravitating system from the present large-scale peculiar velocity or density field. First, a velocity-potential field is extracted from the observed velocities as in the POTENT procedure, or from the density as in the analysis of IRAS redshift surveys, assuming that the velocity field, smoothed on a scale of a few megaparsecs, is irrotational. Then, assuming the Zel'dovich approximation with no orbit crossing, the potential is traced back in time by integrating a simple differential equation in Eulerian space-the Zel'dovich-Bernoulli equation. Finally, the linear velocity and density fields are computed from the linear potential by differentiation. A correction factor for the effect of smoothing velocities over many streams is derived empirically from simulations. The method is demonstrated to reconstruct the initial conditions of an N-body simulation, recovering in particular the initial Gaussian distribution of densities; the initial hills are lower and the valleys are deeper than predicted by linear theory. As an illustration of a possible application we present maps of the initial density field in our local cosmological neighborhood based on the POTENT and IRAS analysis.