Inflation, quantum fluctuations and cosmological perturbations

TL;DR

The paper surveys the standard cosmological framework for the very early universe, highlighting how inflation resolves key puzzles of the Big Bang model and naturally generates primordial perturbations. It develops the scalar field dynamics under slow-roll, derives the horizon-scale evolution of perturbations, and connects quantum fluctuations during inflation to observable power spectra via the Mukhanov variable and the comoving curvature perturbation. It then presents the predictions for scalar and tensor spectra, including the scalar tilt n_s, tensor tilt n_T, and the consistency relation r = 16 εV, while also discussing initial conditions, gauge issues, and super-Hubble evolution. The discussion extends to tensor modes and multi-field scenarios, emphasizing how observations of the CMB and large-scale structure constrain inflationary models and the underlying high-energy physics driving the early universe.

Abstract

These lectures are intended to give a pedagogical introduction to the main current picture of the very early universe. After elementary reviews of general relativity and of the standard Big Bang model, the following subjects are discussed: inflation, the classical relativistic theory of cosmological perturbations and the generation of perturbations from scalar field quantum fluctuations during inflation.