TASI Lectures on Inflation

TL;DR

This work presents a pedagogical overview of cosmological inflation, starting from general relativity and FRW cosmology to motivate inflation as a solution to the horizon and flatness problems. It develops the slow-roll scalar-field framework, derives key parameters ε and η, and explains how inflation ends with reheating to reconnect to the hot Big Bang. The perturbation theory is developed for quantum fluctuations during inflation, yielding nearly scale-invariant scalar and tensor power spectra characterized by P_R(k), P_T(k), and the observables n_S, n_T, and r, with the single-field consistency relation r = 16ε. Observational constraints from WMAP (and Planck-era expectations) favor a red, nearly scale-invariant spectrum with small tensor contributions, supporting inflation while leaving room for future refinement and discrimination among models. Overall, the paper ties high-energy inflationary physics to precision cosmology, highlighting how CMB measurements probe the physics of the very early universe at near-GUT scales.

Abstract

This series of lectures gives a pedagogical review of the subject of cosmological inflation. I discuss Friedmann-Robertson-Walker cosmology and the horizon and flatness problems of the standard hot Big Bang, and introduce inflation as a solution to those problems, focusing on the simple scenario of inflation from a single scalar field. I discuss quantum modes in inflation and the generation of primordial tensor and scalar fluctuations. Finally, I provide comparison of inflationary models to the WMAP satellite measurement of the Cosmic Microwave Background, and briefly discuss future directions for inflationary physics. The majority of the lectures should be accessible to advanced undergraduates or beginning graduate students with only a background in Special Relativity, although familiarity with General Relativity and quantum field theory will be helpful for the more technical sections.

Figures (25)

• Figure 1: Light cones in Minkowski Space. The past light cone defines the causal past of the event $P$, and the future light cone defines the causal future of $P$.
• Figure 2: A comoving box full of matter. The energy density in matter scales inversely with the volume of the box.
• Figure 3: A comoving box full of radiation. The number density of photons scales inversely with the volume of the box, but the photons also increase in wavelength.
• Figure 4: A comoving box full of vacuum. The energy density of vacuum does not scale at all!
• Figure 5: Schematic diagram of how the three types of stress-energy scale with redshift $1 + z \propto a$: at early time, radiation dominates, followed by matter, and finally the universe is dominated by vacuum energy.