Abstract: In a series of five lectures I review inflationary cosmology. I begin with a description of the initial conditions problems of the Friedmann-Robertson-Walker (FRW) cosmology and then explain how inflation, an early period of accelerated expansion, solves these problems. Next, I describe how inflation transforms microscopic quantum fluctuations into macroscopic seeds for cosmological structure formation. I present in full detail the famous calculation for the primordial spectra of scalar and tensor fluctuations. I then define the inverse problem of extracting information on the inflationary era from observations of cosmic microwave background fluctuations. The current observational evidence for inflation and opportunities for future tests of inflation are discussed. Finally, I review the challenge of relating inflation to fundamental physics by giving an account of inflation in string theory.
Lecture 1: Classical Dynamics of Inflation
The aim of this lecture is a first-principles introduction to the classical dynamics of inflationary cosmology. After a brief review of basic FRW cosmology we show that the conventional Big Bang theory leads to an initial conditions problem: the universe as we know it can only arise for very special and finely-tuned initial conditions. We then explain how inflation (an early period of accelerated expansion) solves this initial conditions problem and allows our universe to arise from generic initial conditions. We describe the necessary conditions for inflation and explain how inflation modifies the causal structure of spacetime to solve the Big Bang puzzles. Finally, we end this lecture with a discussion of the physical origin of the inflationary expansion.
Lecture 2: Quantum Fluctuations during Inflation
In this lecture we review the famous calculation of the primordial fluctuation spectra generated by quantum fluctuations during inflation. We present the calculation in full detail and try to avoid `cheating' and approximations. After a brief review of fundamental aspects of cosmological perturbation theory, we first give a qualitative summary of the basic mechanism by which inflation converts microscopic quantum fluctuations into macroscopic seeds for cosmological structure formation. As a pedagogical introduction to quantum field theory in curved spacetime we then review the quantization of the simple harmonic oscillator. We emphasize that a unique vacuum state is chosen by demanding that the vacuum is the minimum energy state. We then proceed by giving the corresponding calculation for inflation. We calculate the power spectra of both scalar and tensor fluctuations.
Lecture 3: Contact with Observations
In this lecture we describe the inverse problem of extracting information on the inflationary perturbation spectra from observations of the cosmic microwave background and the large-scale structure. We define the precise relations between the gauge-invariant scalar and tensor power spectra computed in the previous lecture and the observed CMB anisotropies and galaxy power spectra. We give the transfer functions that relate the primordial fluctuations to the late-time observables. We then use these results to discuss the current observational evidence for inflation. Finally, we indicate opportunities for future tests of inflation.
Lecture 4: Primordial Non-Gaussianity
In this lecture we summarize key theoretical results in the study of primordial non-Gaussianity. Most results are stated without proof, but their significance for constraining the fundamental physical origin of inflation is explained. After introducing the bispectrum as a basic diagnostic of non-Gaussian statistics, we show that its momentum dependence is a powerful probe of the inflationary action. Large non-Gaussianity can only arise if inflaton interactions are significant during inflation. In single-field slow-roll inflation non-Gaussianity is therefore predicted to be unobservably small, while it can be significant in models with multiple fields, higher-derivative interactions or non-standard initial states. Finally, we end the lecture with a discussion of the observational prospects for detecting or constraining primordial non-Gaussianity.
Lecture 5: Inflation in String Theory
We end this lecture series with a discussion of a slightly more advanced topic: inflation in string theory. We provide a pedagogical overview of the subject based on a recent review article with Liam McAllister. The central theme of the lecture is the sensitivity of inflation to Planck-scale physics, which we argue provides both the primary motivation and the central theoretical challenge for realizing inflation in string theory. We illustrate these issues through two case studies of inflationary scenarios in string theory: warped D-brane inflation and axion monodromy inflation. Finally, we indicate opportunities for future progress both theoretically and observationally.
The paper is in pdf format.