Published in the International Journal of Modern Physics D, Volume 9, Issue 04, pp. 373-443 (2000).

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**Abstract.** Recent observations of Type 1a supernovae indicating an
accelerating universe have once more drawn attention to the
possible existence, at the present epoch, of a small positive
-term
(cosmological constant). In this paper we
review both observational and theoretical aspects of a small cosmological
-term. We discuss
the current observational situation focusing on cosmological tests of
including the age
of the universe, high redshift supernovae,
gravitational lensing, galaxy clustering and the
cosmic microwave background. We also review the theoretical debate
surrounding :
the generation of
in models with spontaneous symmetry breaking and
through quantum vacuum polarization effects - mechanisms
which are known to give rise to a
large value of
hence leading to the `cosmological constant problem'.
More recent attempts to generate a small
cosmological constant at the present epoch using either field theoretic
techniques, or by modeling a dynamical
-term
by scalar fields are also extensively discussed. Anthropic
arguments favouring a small
-term are briefly
reviewed. A comprehensive bibliography of recent work
on is provided.

**Table of Contents**

- INTRODUCTION
- THE COSMOLOGICAL CONSTANT REVISITED
- FRW COSMOLOGICAL MODELS WITH 0
- OBSERVATIONAL CONSEQUENCES OF A COSMOLOGICAL LAMBDA-TERM
- H
_{0}, q_{0}and the Age of the Universe - The luminosity distance and gravitational lensing
- Type 1a Supernovae and the value of Lambda
- Constraints on Lambda from the cosmic microwave background
- The Angular size - redshift relation
- Clusters of galaxies and the Large Scale Structure of the Universe
- THEORETICAL ISSUES: VACUUM FLUCTUATIONS AND THE COSMOLOGICAL CONSTANT
- THE COSMOLOGICAL CONSTANT AND SPONTANEOUS SYMMETRY BREAKING
- MECHANISMS FOR GENERATING A SMALL CURRENT VALUE OF LAMBDA
- A Decaying Cosmological Constant?
- Vacuum polarization and the value of Lambda
- Late-time Inflation and Lambda.
- Generating a small cosmological constant from Inflationary particle production
- PHENOMENOLOGICAL MODELS OF A DYNAMICAL LAMBDA-TERM
- Overview
- When may a Lambda-term be described by a minimally coupled scalar field?
- Relation between kinematic and dynamical descriptions of Lambda
- Reconstructing the effective potential V()
- UNIVERSALITY OF LAMBDA AND ANTHROPIC ARGUMENTS FOR ITS SMALL VALUE
- SUMMARY AND DISCUSSION
- REFERENCES