Reconstruction of primordial density fields

The Monge-Ampere-Kantorovich (MAK) reconstruction is tested against cosmological N-body simulations. Using only the present mass distribution sampled with particles, and the assumption of homogeneity of the primordial distribution, MAK recovers for each particle the non-linear displacement field between its present position and its Lagrangian position on a primordial uniform grid. To test the method, we examine a standard Lambda cold dark matter (Lambda CDM) N-body simulation with Gaussian initial conditions and six models with non-Gaussian initial conditions: a chi(2) model, a model with primordial voids and four weakly non-Gaussian models. Our extensive analyses of the Gaussian simulation show that the level of accuracy of the reconstruction of the non-linear displacement field achieved by MAK is unprecedented, at scales as small as similar to 3 h(-1) Mpc. In particular, it captures in a non-trivial way the non-linear contribution from gravitational instability, well beyond the Zel'dovich approximation. This is also confirmed by our analyses of the non-Gaussian samples. Applying the spherical collapse model to the probability distribution function of the divergence of the displacement field, we also show that from a well-reconstructed displacement field, such as that given by MAK, it is possible to accurately disentangle dynamical contributions induced by gravitational clustering from possible initial non-Gaussianities, allowing one to efficiently test the non-Gaussian nature of the primordial fluctuations. In addition, we test successfully a simple application of MAK using the Zel'dovich approximation to recover in real space the present-day peculiar velocity field on scales of 8 h(-1) Mpc. Although non-trivial observational issues yet remain to be addressed, our numerical investigations suggest that MAK reconstruction represents a very promising tool to be applied to three-dimensional Galaxy catalogues.