Reconstruction of primordial density fields

• Published in: Monthly notices of the Royal Astronomical Society Vol. 365; no. 3; pp. 939 - 959
• Main Authors: Mohayaee, Roya, Mathis, Hugues, Colombi, Stéphane, Silk, Joseph
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Science Ltd 01.01.2006; Blackwell Science; Oxford University Press
• Subjects: Astronomy; Cosmology; Dark matter; Earth, ocean, space; Exact sciences and technology; large-scale structure of Universe; methods: N-body simulations; methods: numerical; Numerical analysis; Simulation; Collapse; methods: N-body simulations; Fluctuations; Lagrangian; Galaxies; Digital simulation; large-scale structure of Universe; Mass distribution; N body system; Probability distribution; Spherical model; Numerical method; Large-scale structure; methods: numerical; Zeldovich approximation; Velocity fields; Divergences; Initial conditions; Dark matter; Gravitational instability; Cold dark matter; Particle distribution; Astronomical catalogues; Positions
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2005.09774.x

The Monge-Ampère-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 (λCDM) N-body simulation with Gaussian initial conditions and six models with non-Gaussian initial conditions: a χ2 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 ∼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.