Dynamics of cosmological perturbations at first and second order

TL;DR

This paper develops minimal, gauge-invariant systems of equations for first and second order scalar cosmological perturbations in flat Friedmann-Lemaître universes, facilitating explicit solutions and broad future applications.

Contribution

It introduces simplified, dimensionless, gauge-invariant systems of equations for cosmological perturbations that are minimal and ready-to-use, improving upon previous formulations.

Findings

Provides explicit systems for super-horizon adiabatic perturbations

Applies to perturbations in $\\Lambda$CDM universes

Serves as a reference framework for future research

Abstract

In this paper we give five gauge-invariant systems of governing equations for first and second order scalar perturbations of flat Friedmann-Lema\^{i}tre universes that are minimal in the sense that they contain no redundant equations or variables. We normalize the variables so that they are dimensionless, which leads to systems of equations that are simple and ready-to-use. We compare the properties and utility of the different systems. For example, they serve as a starting point for finding explicit solutions for two benchmark problems in cosmological perturbation theory at second order: adiabatic perturbations in the super-horizon regime (the long wavelength limit) and perturbations of $\Lambda$CDM universes. However, our framework has much wider applicability and serves as a reference for future work in the field.