Dynamics of cosmological perturbations at first and second order

Abstract

In this paper we give five gauge-invariant systems of governing equations for first and second order scalar perturbations of flat Friedmann-Lemaître 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.

27 pages

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Cited by in corpus (8)

• Analytic solutions of scalar perturbations induced by scalar perturbations
• Perturbations of the Lambda-CDM model in a dynamical systems perspective
• Second order cosmological perturbations: simplified gauge change formulas
• Dynamical systems in perturbative scalar field cosmology
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• The general solution at large scale for second order perturbations in a scalar field dominated universe