COSMIC DENSITY AND VELOCITY-FIELDS IN LAGRANGIAN PERTURBATION-THEORY

A first- and second-order relation between cosmic density and peculiar -velocity fields is presented. The calculation is purely Lagrangian an d it is derived using the second-order solutions of the Lagrange-Newto n system obtained by Buchert & Ehlers. The procedure is applied to two particular solutions given generic initial conditions. In this approa ch, the continuity equation yields a relation between the over-density and peculiar-velocity fields that automatically satisfies Euler's equ ation 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 equatio n in order to calculate a first- or second-order expression for the de nsity field. In these previous schemes, the density contrast given by (a) the continuity equation and (b) Euler's equation are mutually inco mpatible. This inconsistency arises as a consequence of an improper ha ndling of Lagrangian and Eulerian coordinates in the analysis. Here, w e take into account the fact that an exact calculation of the density is feasible in the Lagrangian picture and therefore an accurate and co nsistent description is obtained.