Reconstruction of the primordial Universe by a Monge--Ampere--Kantorovich optimisation scheme

Abstract

A method for the reconstruction of the primordial density fluctuation field is presented. Various previous approaches to this problem rendered {\it non-unique} solutions. Here, it is demonstrated that the initial positions of dark matter fluid elements, under the hypothesis that their displacement is the gradient of a convex potential, can be reconstructed uniquely. In our approach, the cosmological reconstruction problem is reformulated as an assignment problem in optimisation theory. When tested against numerical simulations, our scheme yields excellent reconstruction on scales larger than a few megaparsecs.

arXiv comment14 pages, 10 figures

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• Reconstruction of primordial density fields
• Simulating Structure Formation of the Local Universe
• The Cosmological Mean Density and its Local Variations Probed by Peculiar Velocities
• New method for initial density reconstruction
• Cosmic velocity--gravity relation in redshift space
• A fast semi-discrete optimal transport algorithm for a unique reconstruction of the early Universe
• BAO reconstruction: a swift numerical action method for massive spectroscopic surveys
• Euclid: The search for primordial features
• The non-perturbative regime of cosmic structure formation
• Iterative removal of redshift space distortions from galaxy clustering
• Biased tracer reconstruction with halo mass information
• Performance study of Lagrangian methods: reconstruction of large scale peculiar velocities and baryonic acoustic oscillations
• Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmology
• Lagrangian space remapping and the angular momentum reconstruction from cosmic structures