Lecture Notes on Inflationary Cosmology

Abstract

The temperature fluctuations in the Cosmic Microwave Background (CMB) are a snapshot of the primordial density perturbations that gave rise to structure formation. But… where were these initial fluctuations coming from? In this course, prepared for a graduate level course at the University of Heidelberg and the University of Helsinki, we will discuss the limitations of the hot Big Bang model in addressing this question and its answer within the inflationary paradigm. We will extend the canonical quantization in Minkowski spacetime to extreme cosmological environments, where familiar concepts like “vacuum state” or “particle” become generically ill-defined. Using the resulting formalism, we will present a detailed derivation of the primordial power spectra. In particular, we will show that the quantum-mechanical treatment of inflation leads to an almost scale invariant spectrum of classical density perturbations in excellent agreement with observations and to a (still-undiscovered) gravitational wave background. Finally, we will discuss the transition from the cold and empty post-inflationary Universe to the hot and highly entropic one we observe today. This transition involves rich physics such as Bose enhancement, turbulence and thermalization.