An introduction to inflation and cosmological perturbation theory

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 scalar and 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 good 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.