Fully nonlinear cosmological perturbations of multi-component fluid and field systems

TL;DR

This paper derives fully nonlinear cosmological perturbation equations for multiple fluid and scalar field systems, applicable to general curvature and cosmological constant scenarios, advancing the understanding of nonlinear structure formation.

Contribution

It provides the first comprehensive set of exact nonlinear perturbation equations for multi-component fluids and scalar fields without gauge restrictions, including the Newtonian limit and third-order perturbations.

Findings

Derived exact nonlinear perturbation equations for multiple fluids and scalar fields.

Established the Newtonian limit in specific gauge conditions.

Presented third-order perturbation equations for nonrelativistic pressure fluids.

Abstract

We present fully nonlinear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. For each fluid component we ignore the anisotropic stress. The multiple component nature, however, introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully nonlinear equations and the third-order perturbation equations of the nonrelativistic pressure fluids in the CDM-comoving gauge.