Based on talks given at "Understanding our Universe at the close of the 20th century", Cargese, April 2000. (astro-ph/0009491)

Abstract. The cosmological model best capable of fitting current observational data features two separate epochs during which the Universe is accelerating. During the earliest stages of the Universe, such acceleration is known as cosmological inflation, believed to explain the global properties of the Universe and the origin of structure. Observations of the present state of the Universe strongly suggest that its density is currently dominated by dark energy with properties equivalent or similar to a cosmological constant. In these lecture notes, I provide an introductory account of both topics, including the possibility that the two epochs may share the same physical description, and give an overview of the current status.

Table of Contents

• OVERVIEW
• A HOT BIG BANG REMINDER
• Overview
• Equations of motion
• Standard cosmological solutions
• Critical density and the density parameter
• Characteristic scales and horizons
• Redshift and temperature
• The history of the Universe
• THE INFLATIONARY COSMOLOGY
• The definition of inflation
• Scalar fields and their potentials
• Models of inflation
• Equations of motion and solutions
• The relation between inflation and slow-roll
• The amount of inflation
• A worked example: polynomial chaotic inflation
• Multi-field theories
• Reheating after inflation
• DENSITY PERTURBATIONS AND GRAVITATIONAL WAVES
• Production during inflation
• A worked example
• Observational consequences
• Testing the idea of inflation
• Growing mode perturbations
• Gaussianity and adiabaticity
• Tensor and vector modes
• Power-law spectra
• ACCELERATION IN THE PRESENT UNIVERSE
• Cosmological constant: exact or effective?
• Scaling solutions and trackers
• Challenges for quintessence
• SUMMARY
• REFERENCES