An introduction to inflation and cosmological perturbation theory

TL;DR

This paper provides an introductory overview of inflation and cosmological perturbation theory, explaining how inflation generates nearly scale-invariant perturbations consistent with cosmic microwave background observations.

Contribution

It offers a comprehensive, accessible review of inflationary theory, perturbation equations, and observational constraints, suitable for newcomers to the field.

Findings

Inflation naturally produces an almost scale-invariant spectrum of perturbations.

Recent observations strongly support the inflationary paradigm.

Constraints on inflation models are discussed based on current data.

Abstract

This article provides an introductory review of inflation and cosmological perturbation theory. I begin by motivating the need for an epoch of inflation during the early stages of the radiation dominated era, and describe how inflation is typically achieved using scalar fields. Then, after an overview of linear cosmological perturbation theory, I derive the equations governing the perturbations, and outline the generation of the scalar and the tensor perturbations during inflation. I illustrate that slow roll inflation naturally leads to an almost scale invariant spectrum of perturbations, a prediction that seems to be in remarkable agreement with the measurements of the anisotropies of the cosmic microwave background. I describe the constraints from the recent observations on some of the more popular models of inflation. I conclude with a brief discussion on the status and certain prospects of the inflationary paradigm.