A simplified structure for the second order cosmological perturbation equations

TL;DR

This paper introduces a simplified, flexible framework for deriving second order cosmological perturbation equations, making it easier to analyze nonlinear effects in the universe's structure formation.

Contribution

It presents a minimal and general derivation of second order perturbation equations in cosmology, adaptable to various gauges and stress-energy tensors.

Findings

Simplified equations facilitate nonlinear cosmological perturbation analysis.

Framework applicable to any stress-energy content.

Compatible with multiple gauge choices.

Abstract

Increasingly accurate observations of the cosmic microwave background and the large scale distribution of galaxies necessitate the study of nonlinear perturbations of Friedmann-Lemaitre cosmologies, whose equations are notoriously complicated. In this paper we present a new derivation of the governing equations for second order perturbations within the framework of the metric-based approach that is minimal, as regards amount of calculation and length of expressions, and flexible, as regards choice of gauge and stress-energy tensor. Because of their generality and the simplicity of their structure our equations provide a convenient starting point for determining the behaviour of nonlinear perturbations of FL cosmologies with any given stress-energy content, using either the Poisson gauge or the uniform curvature gauge.