The Monge-Ampère-Kantorovich approach to reconstruction in cosmology

Roya Colin Mohayaee, Institut d'Astrophysique de Paris

With Andreĭ Sobolevskiĭ, Moscow State University and IIEPT, Moscow

Reconstructing the density fluctuations in the early Universe that evolved into the distribution of galaxies we see today is a challenge to modern cosmology. An accurate reconstruction allows us to test cosmological models and put tighter constraints on cosmological parameters. Several reconstruction techniques have been proposed, but they all suffer from lack of uniqueness. Here we show that within a reasonable approximation reconstruction can be reduced to a well-determined problem of optimization, and present a specific algorithm that provides excellent agreement when tested against data from N-body simulations.

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