The recursion relation in Lagrangian perturbation theory
  We derive a recursion relation in the framework of Lagrangian perturbation
theory, appropriate for studying the inhomogeneities of the large scale
structure of the universe. We use the fact that the perturbative expansion of
the matter density contrast is in one-to-one correspondence with standard
perturbation theory (SPT) at any order. This correspondence has been recently
shown to be valid up to fourth order for a non-relativistic, irrotational and
dust-like component. Assuming it to be valid at arbitrary (higher) order, we
express the Lagrangian displacement field in terms of the perturbative kernels
of SPT, which are itself given by their own and well-known recursion relation.
We argue that the Lagrangian solution always contains more non-linear
information in comparison with the SPT solution, (mainly) if the
non-perturbative density contrast is restored after the displacement field is
obtained.
