A Concise Introduction to Perturbation Theory in Cosmology

TL;DR

This paper provides a clear and self-contained overview of perturbation theory in cosmology, focusing on linear and second order calculations, gauge issues, and gauge-invariant variables.

Contribution

It introduces a balanced, accessible approach to cosmological perturbation theory, including gauge transformations and second order tensor perturbations.

Findings

Constructed gauge-invariant variables for second order perturbations

Clarified gauge transformation approaches in cosmological perturbation theory

Presented a self-contained, rigorous introduction to the topic

Abstract

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.