Application of optimal transport theory to reconstruction of the early Universe

The problem of deterministic reconstruction of the past kinetic history of the Universe is shown to be reduced, within the Zel'dovich approximation, to solving a Monge–Ampère equation. A variational representation, due to Y. Brenier, is then employed to devise a “Monge–Ampère–Kantorovich” numerical method of cosmological reconstruction. Results of testing and application of this method are discussed.