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Astron. Astrophys. 323, 295-304 (1997)

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Cosmic density and velocity fields in Lagrangian perturbation theory

Mikel Susperregi 1 and Thomas Buchert 2

1 Astronomy Unit, School of Mathematical Sciences, Queen Mary & Westfield, London E1 4NS, UK (mps@maths.qmw.ac.uk)
2 Theoretische Physik, Ludwig-Maximilians-Universität, Theresienstr. 37, D-80333 München, Germany (buchert@stat.physik.uni-muenchen.de)

Received 23 May 1996 / Accepted 16 December 1996


A first- and second-order relation between cosmic density and peculiar-velocity fields is presented. The calculation is purely Lagrangian and it is derived using the second-order solutions of the Lagrange-Newton system obtained by Buchert & Ehlers. The procedure is applied to two particular solutions given generic initial conditions. In this approach, the continuity equation yields a relation between the over-density and peculiar-velocity fields that automatically satisfies Euler's equation because the orbits are derived from the Lagrange-Newton system. This scheme generalizes some results obtained by Nusser et al. (1991) in the context of the Zel'dovich approximation. As opposed to several other reconstruction schemes, in this approach it is not necessary to truncate the expansion of the Jacobian given by the continuity equation in order to calculate a first- or second-order expression for the density field. In these previous schemes, the density contrast given by (a) the continuity equation and (b) Euler's equation are mutually incompatible. This inconsistency arises as a consequence of an improper handling of Lagrangian and Eulerian coordinates in the analysis. Here, we take into account the fact that an exact calculation of the density is feasible in the Lagrangian picture and therefore an accurate and consistent description is obtained.

Key words: cosmology: theory – large-scale structure of the universe


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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998