In "High Energy Physics and Cosmology", 1999,
eds. A. Masiero, G. Senjanovic, and A. Smirnov

# AN INTRODUCTION TO COSMOLOGICAL INFLATION

### Andrew R. Liddle

Astronomy Centre,
University of Sussex,
Brighton BN1 9QJ, U. K.

and

Astrophysics
Group, The Blackett Laboratory, Imperial College,

London
SW7 2BZ, U. K. (present address)

**Abstract.** An introductory account is given of the inflationary
cosmology, which postulates a period of accelerated
expansion during the Universe's earliest stages. The historical
motivation is briefly outlined, and the modelling of the inflationary
epoch explained. The most important aspect of inflation is that it
provides a possible model for the origin of structure in the Universe,
and key results are reviewed, along with a discussion of the current
observational situation and outlook.

**Table of Contents**

- OVERVIEW

- BIG BANG PROBLEMS AND THE IDEA OF INFLATION
- A hot big bang reminder
- Equations of motion
- Standard cosmological solutions
- Critical density and the density parameter
- Characteristic scales and horizons
- Redshift and temperature
- The history of the Universe

- PROBLEMS WITH THE BIG BANG
- The flatness problem
- The horizon problem
- The monopole problem (and other relics)

- THE IDEA OF INFLATION
- The flatness problem
- Relic abundances
- The horizon problem and homogeneity

- MODELLING THE INFLATIONARY EXPANSION
- Scalar fields and their potentials
- 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
- The range of inflation models
- Chaotic inflation models
- Multi-field theories
- Beyond general relativity
- Open inflation

- Recap

- DENSITY PERTURBATIONS AND GRAVITATIONAL WAVES
- Production during inflation
- A worked example
- Observational consequences
- Testing the idea of inflation

- THE INFLATIONARY ORIGIN OF STRUCTURE
- The parameters
- The inflationary energy scale
- Beyond the energy scale

- SUMMARY

- REFERENCES