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Applied Math Seminar
Reconstruction of the Early Universe as a Monge-Ampere-Kantorovich
Mass Transportation Problem
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The Monge-Kantorovich mass transportation problem dates back to work by Monge in 1781 on how to optimally move material from one place to another, knowing only its initial and final spatial distributions, the cost being a prescribed function of the distance travelled by "molecules" of material. Here we solve the fluid-dynamical cosmological reconstruction problem of mapping the present locations of matter, to their primordial locations, knowing only the current field of mass density, e.g. from a full-sky galaxy catalogue or a numerical simulation. On sufficiently large scales (a few megaparsecs) the reconstruction problem becomes a mass transportation problem which can be solved by very efficient optimisation algorithms. |