Geodesic
Application of optimal transport theory to reconstruction of the early Universe
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part XI, Tome 312 (2004), pp. 303-309 
A. N. Sobolevskii; U. Frisch. Application of optimal transport theory to reconstruction of the early Universe. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part XI, Tome 312 (2004), pp. 303-309. http://geodesic.mathdoc.fr/item/ZNSL_2004_312_a20/
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     author = {A. N. Sobolevskii and U. Frisch},
     title = {Application of optimal transport theory to reconstruction of the early {Universe}},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_312_a20/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] E. Bertschinger, A. Dekel, “Recovering the full velocity and density fields from large-scale redshift-distance samples”, Astrophys. J., 336 (1989), L5–L8 | DOI

[2] D. Bertsekas, “Auction algorithms for network flow problems: a tutorial introduction”, Comput. Optim. Appl., 1 (1992), 7–66 | MR | Zbl

[3] Y. Brenier, “Polar factorization and monotone rearrangement of vector-valued functions”, Comm. Pure Appl. Math., 44 (1991), 375–417 | DOI | MR | Zbl

[4] Y. Brenier, U. Frisch, M. Hénon, G. Loeper, S. Matarrese, R. Mohayaee, A. Sobolevskiĭ, “Reconstruction of the early universe as a convex optimization problem”, Mon. Not. R. Astron. Soc., 346 (2003), 501–524 | DOI

[5] R. E. Burkard, “Selected topics on assignment problems”, Discrete Appl. Math., 123:1–3 (2002), 257–302 | DOI | MR | Zbl

[6] U. Frisch, S. Matarrese, R. Mohayaee, A. Sobolevski, “A reconstruction of the initial conditions of the Universe by optimal mass transportation”, Nature, 417 (2002), 260–262 | DOI

[7] G. Loeper, “The inverse problem for the Euler–Poisson system in cosmology”, Arch. Rat. Mech. Anal., 2004 (to appear) | Zbl

[8] R. Mohayaee, R. Brent Tully, U. Frisch, “Reconstruction of large-scale peculiar velocity fields”, Cosmology: Facts and Problems (College de France, Paris, 8–11 June 2004), eds. J. V. Narlikar, J.-C. Pecker (eds.)

[9] P. Peebles, The Large-Scale Structure of the Universe, Princeton University Press, Princeton, NJ, 1980 | MR

[10] R. Brent Tully, Nearby Galaxies Catalog., Cambridge University Press, Cambridge and New York, 1988

[11] Y. Zel'dovich, “Gravitational instability: an approximate theory for large density perturbations”, Astron. and Astrophys., 5 (1970), 84–89