Application of gradient expansion to non-linear gravitational wave in plane-symmetric universe

TL;DR

This paper applies the gradient expansion method to analyze non-linear gravitational waves in a plane-symmetric universe, revealing the significance of non-linear effects during anisotropic stages and confirming linear perturbation results.

Contribution

It introduces a second-order gradient expansion approach to study non-linear gravitational waves in a plane-symmetric cosmological model.

Findings

Non-linear effects are crucial during anisotropic universe stages.

Second-order expansion captures non-linear gravitational wave perturbations.

Linear source term perturbations align with linear perturbation theory results.

Abstract

As an application of Gradient Expansion (long-wavelength) approximation, we studied the inhomogeneous universe including the gravitational wave(GW). For a plane-symmetric cosmological model, we could implement the 2nd order expansion and analyze the purely non-linear perturbation of GW. The result indicates that the non-linear effect plays an important role in anisotropic stage of the universe. We also confirm that the perturbation from the linear source term in gradient expansion is consistent with the result of linear perturbation.