Invited Review for Physics Reports.
hep-th/0212290.

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Abstract. Recent cosmological observations suggest the existence of a positive cosmological constant with the magnitude (G / c³) 10^-123. This review discusses several aspects of the cosmological constant both from the cosmological (sections 1 - 6) and field theoretical (sections 7 - 11) perspectives. The first section introduces the key issues related to cosmological constant and provides a brief historical overview. This is followed by a summary of the kinematics and dynamics of the standard Friedmann model of the universe paying special attention to features involving the cosmological constant. Section 3 reviews the observational evidence for cosmological constant, especially the supernova results, constraints from the age of the universe and a few others. Theoretical models (quintessence, tachyonic scalar field, ...) with evolving cosmological `constant' are described from different perspectives in the next section. Constraints on dark energy from structure formation and from CMBR anisotropies are discussed in the next two sections. The latter part of the review (sections 7 - 11) concentrates on more conceptual and fundamental aspects of the cosmological constant. Section 7 provides some alternative interpretations of the cosmological constant which could have a bearing on the possible solution to the problem. Several relaxation mechanisms have been suggested in the literature to reduce the cosmological constant to the currently observed value and some of these attempts are described in Section 8. Next section gives a brief description of the geometrical structure of the de Sitter spacetime and the thermodynamics of the de Sitter universe is taken up in section 10. The last section deals with the role of string theory in the cosmological constant problem.

Key words: cosmological constant, dark energy, cosmology, cmbr, quintessence, de Sitter spacetime, horizon, tachyon, string theory
PACS: 98.80.-k, 98.80.Es , 98.80.Cq , 98.80.Qc , 04.60.-m

Table of Contents

INTRODUCTION

The many faces of the cosmological constant

A brief history of cosmological constant

FRAMEWORK OF STANDARD COSMOLOGY

Kinematics of the Friedmann model

Dynamics of the Friedmann model

Composition of the universe

Geometrical features of a universe with a cosmological constant

EVIDENCE FOR A NON-ZERO COSMOLOGICAL CONSTANT

Observational evidence for accelerating universe

Age of the universe and cosmological constant

Gravitational lensing and the cosmological constant

Other geometrical tests

MODELS WITH EVOLVING COSMOLOGICAL "CONSTANT"

Parametrized equation of state and cosmological observations

Theoretical models with time dependent dark energy: cosmic degeneracy

STRUCTURE FORMATION IN THE UNIVERSE

Linear evolution of perturbations

Nonlinear growth of perturbations

Structure formation and constraints on dark energy

CMBR ANISOTROPIES

REINTERPRETING THE COSMOLOGICAL CONSTANT

Cosmological constant as a Lagrange multiplier

Cosmological constant as a constant of integration

Cosmological constant as a stochastic variable

Anthropic interpretation of the cosmological constant

Probabilistic interpretation of the cosmological constant

RELAXATION MECHANISMS FOR THE COSMOLOGICAL CONSTANT

GEOMETRICAL STRUCTURE OF THE DE SITTER SPACETIME

HORIZONS, TEMPERATURE AND ENTROPY

The connection between thermodynamics and spacetime geometry

Temperature of horizons

Entropy and energy of de Sitter spacetime

Conceptual issues in de Sitter thermodynamics

COSMOLOGICAL CONSTANT AND THE STRING THEORY

REFERENCES