Lagrangian theory of gravitational instability of FriedmanLemaitre cosmologies  secondorder approach: an improved model for nonlinear clustering
Abstract
A large class of solutions for secondorder irrotational perturbations is derived in the framework of the Lagrangian theory of gravitational instability of a homogeneous and isotropic universe investigated in earlier papers. The solutions are evaluated in detail for perturbations in a flat background universe. The form of the solutions is designed for use in studies of the formation of largescale structure from generic initial conditions. Some general remarks on the properties of the solutions are made. The result is illustrated by a special case and discussed. In particular, it is found that sheetlike structures stay compact after shellcrossing (as in the competing `adhesion model'), and that the collapse of first objects occurs earlier (as expected from numerical simulations) in the secondorder approach. Both these properties compensate shortcomings of the `Zel'dovich approximation'. In contrast to the `adhesion model', the nthorder Lagrangian perturbation solutions also describe internal structures of selfgravitating pancakes (=2n + 1 stream systems) in terms of the nth orbit crossings within pancakes.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 1993
 DOI:
 10.1093/mnras/264.2.375
 Bibcode:
 1993MNRAS.264..375B
 Keywords:

 instabilities  methods: analytical  galaxies: clustering  cosmology: theory  largescale structure of Universe