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
- Reheating after inflation
- DENSITY PERTURBATIONS AND GRAVITATIONAL WAVES
- Production during inflation
- A worked example
- Observational consequences
- Testing the idea of inflation
- ACCELERATION IN THE PRESENT UNIVERSE
- Cosmological constant: exact or effective?
- Scaling solutions and trackers
- Challenges for quintessence
- SUMMARY
- REFERENCES