Higher--Order Lagrangian Perturbation Theory

Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On its basis a Lagrangian perturbation approach is discussed and compared with the standard Eulerian theory of gravitational instability. The performance of Lagrangian perturbation solutions up to the third order is demonstrated in comparison with numerical N-body simulations. First results of this comparison are presented for large scales (PM-code) and for small scales (tree-code).