Fourth-order perturbative equations in lagrangian perturbation theory for a cosmological dust fluid

Abstract

We have derived fourth-order perturbative equations in Lagrangian perturbation theory for a cosmological dust fluid. These equations are derived under the supposition of Newtonian cosmology in the Friedmann-Lemaître- Robertson-Walker Universe model. Even if we consider the longitudinal mode in the first-order perturbation, the transverse mode appears in the third-order perturbation. Furthermore, in this case, six longitudinal-mode equations and four transversemode equations appear in the fourth-order perturbation. The application of the fourth-order perturbation leads to a precise prediction of the large-scale structure. © The Author(s) 2013..