Reconstruction of cosmological density and velocity fields in the Lagrangian Zel'dovich approximation

We present a method for reconstructing cosmological density and velocity fields using the Lagrangian Zel'dovich formalism. The method involves finding the least-action solution for straight-line particle paths in an evolving density field. Our starting point is the final, evolved density, so that we are in effect carrying out the standard Zel'dovich approximation based process in reverse. Using a simple numerical algorithm we are able to minimize the action for the trajectories of several million particles. We apply our method to the evolved density taken from N-body simulations of different cold dark matter (CDM)-dominated universes, testing both the prediction for the present-day velocity field and that for the initial density field. The method is easy to apply, reproduces the accuracy of the forward Zel'dovich approximation, and also works directly in redshift-space with minimal modification.