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

TL;DR

This paper derives fourth-order Lagrangian perturbation equations for a cosmological dust fluid within Newtonian cosmology, enhancing the precision of large-scale structure predictions.

Contribution

It presents the first derivation of fourth-order perturbative equations in Lagrangian theory for cosmological dust, including transverse modes.

Findings

Inclusion of transverse modes at third and fourth order.

Six longitudinal and four transverse equations at fourth order.

Improved accuracy in large-scale structure modeling.

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-Lema\^{i}tre-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 transverse-mode equations appear in the fourth-order perturbation. The application of the fourth-order perturbation leads to a precise prediction of the large-scale structure.