TASI Lectures on Inflation

TL;DR

The TASI Lectures on Inflation provide a comprehensive, step-by-step exposition of the inflationary paradigm, starting from the classical FRW background and its initial-condition problems, through the quantum generation of primordial scalar and tensor fluctuations, to their observational manifestations in the CMB and LSS. The text derives the primordial power spectra using the Mukhanov–Sasaki formalism, clarifies how these spectra map to CMB observables via transfer functions, and discusses current and future tests including tensor modes and non-Gaussianity. It also surveys model-building aspects, from single-field slow-roll dynamics to multi-field and non-canonical scenarios, and culminates with the challenge of embedding inflation in string theory. Altogether, the notes connect high-energy physics to cosmological data, offering a rigorous framework for diagnosing the physics of the early universe and guiding future experimental tests. The material emphasizes the coherence and phase information imprinted by inflation, the predictive power of slow-roll relations, and the crucial role of polarization as a probe of primordial gravitational waves.

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.

Figures (38)

• Figure 1: Fluctuations in the Cosmic Microwave Background (CMB). What produced them?
• Figure 2: History of the universe. In this schematic we present key events in the history of the universe and their associated time and energy scales. We also illustrate several cosmological probes that provide us with information about the structure and evolution of the universe. Acronyms: BBN (Big Bang Nucleosynthesis), LSS (Large-Scale Structure), BAO (Baryon Acoustic Oscillations), QSO (Quasi-Stellar Objects = Quasars), Ly$\alpha$ (Lyman-alpha), CMB (Cosmic Microwave Background), Ia (Type Ia supernovae), 21cm (hydrogen 21cm-transition).
• Figure 3: Light cones and causality. Photons travel along world lines of zero proper time, ${\rm d} s^2 =0$, called null geodesics. Massive particles travel along world lines with real proper time, ${\rm d} s^2 > 0$, called timelike geodescis. Causally disconnected regions of spacetime are separated by spacelike intervals, ${\rm d} s^2 < 0$. The set of all null geodesics passing through a given point (or event) in spacetime is called the light cone. The interior of the light cone, consisting of all null and timelike geodesics, defined the region of spacetime causally related to that event.
• Figure 4: A combination CMB and LSS observations indicate that the spatial geometry of the universe is flat WMAP5. Note that the evidence for flatness cannot be obtained from CMB observations alone.
• Figure 5: Evidence for dark energy. Shown are a combination of observations of the cosmic microwave background (CMB), supernovae (SNe) and baryon acoustic oscillations (BAO) unionsn.