From inflation to hot big bang -- a tutorial on cosmological perturbations

Abstract

These lecture notes are meant as a pedagogic guide to cosmological inflation and the early epochs thereafter. Inflation explains how the seeds for density perturbations, which evolved into the largest structures in our universe, could have formed during a period of exponential expansion. Apart from density perturbations, also tensor perturbations are generated, which may be observed as gravitational waves. The formalism is developed through explicit computations, paying attention to general-relativistic gauge invariance, and to thermalization (the mechanism that converts part of the energy density driving exponential expansion into the conventional hot big bang). For the steps best handled numerically or computer-algebraically, simple python scripts are provided. We aim at an unassuming style, hopefully accessible to students of theoretical high-energy physics.