EDP Sciences
Free access
Volume 406, Number 2, August I 2003
Page(s) 393 - 401
Section Extragalactic astronomy
DOI http://dx.doi.org/10.1051/0004-6361:20030719

A&A 406, 393-401 (2003)
DOI: 10.1051/0004-6361:20030719

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

R. Mohayaee1, U. Frisch1, S. Matarrese2 and A. Sobolevskii1, 3

1  Département Cassini, Observatoire de la Côte d'Azur, BP 4229, 06304 Nice Cedex 4, France
2  Dipartimento di Fisica "Galileo Galilei" and INFN, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
3  Department of Physics, M. V. Lomonossov Moscow State University, 119992 Moscow, Russia

(Received 12 March 2003 / Accepted 12 May 2003)

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.

Key words: reconstruction -- Lagrangian methods -- convexity -- optimization

Offprint request: R. Mohayaee, roya@obs-nice.fr

© ESO 2003