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