Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background

TL;DR

This paper extends fully nonlinear cosmological perturbation equations to include background curvature, providing a gauge-ready formulation applicable to various gauge choices and perturbation types.

Contribution

It introduces a comprehensive nonlinear perturbation framework for non-flat Friedmann backgrounds, accommodating scalar, vector, and scalar field perturbations.

Findings

Perturbation equations explicitly include background curvature effects.

Framework applicable to any gauge choice for nonlinear cosmological analysis.

Formulation covers scalar, vector, and scalar field perturbations.

Abstract

We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. %The background curvature term explicitly appears only in the energy and momentum constraint equations. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.