Reconstruction of cosmological initial conditions from galaxy redshift catalogues

We present and test a new method for the reconstruction of cosmological ini tial conditions from a full-sky galaxy catalogue. This method, called ZTRAC E, is based on a self-consistent solution of the growing mode of gravitatio nal instabilities according to the Zel'dovich approximation and higher orde r in Lagrangian perturbation theory. Given the evolved redshift-space densi ty field, smoothed on some scale, ZTRAGE finds, via an iterative procedure, an approximation to the initial density field for any given set of cosmolo gical parameters; real-space densities and peculiar velocities are also rec onstructed. The method is tested by applying it to N-body simulations of an Einstein-de Sitter and an open cold dark matter universe. It is shown that errors in the estimate of the density contrast dominate the noise of the r econstruction. As a consequence, the reconstruction of real-space density a nd peculiar velocity fields using non-linear algorithms is little improved over those based on linear theory. The use of a mass-preserving adaptive sm oothing, equivalent to a smoothing in Lagrangian space, allows an unbiased (although noisy) reconstruction of initial conditions, as long as the (line arly extrapolated) density contrast does not exceed unity. The probability distribution function of the initial conditions is recovered to high precis ion, even for Gaussian smoothing scales of similar to 5h(-1) Mpc, except fo r the tail at delta greater than or equal to 1. This result is insensitive to the assumptions of the background cosmology.