Back to the primordial Universe by a Monge-Ampère-Kantorovich optimization scheme

A new method for reconstruction of the primordial density fluctuation field is presented. Various previous approaches to this problem rendered 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 optimization theory. When tested against numerical simulations, our scheme yields excellent reconstruction on scales larger than a few megaparsecs.