An improved reconstruction method for cosmological density fields

This paper proposes some improvements to existing reconstruction methods for recovering the initial linear density and velocity fields of the universe from the present large-scale density distribution. We derive the Eulerian continuity equation in the Zel'dovich approximation and show that, by applying this equation, we can trace the evolution of the gravitational potential of the universe more exactly than is possible with previous approaches based on the Zel'dovich-Bernoulli equation. The improved reconstruction method is tested using N-body simulations. When the Zel'dovich-Bernoulli equation describes the formation of filaments, then the Zel'dovich continuity equation also follows the clustering of clumps inside the filaments. Our reconstruction method recovers the true initial gravitational potential with an rms error about 3 times smaller than previous methods. We examine the recovery of the initial distribution of Fourier components and find the scale at which the recovered phases are scrambled with respect their true initial values. Integrating the Zel'dovich continuity equation back in time, we can improve the spatial resolution of the reconstruction by a factor of about 2.