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

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COSMOLOGICAL CONSTANT - THE WEIGHT OF THE VACUUM

T. Padmanabhan


IUCAA, Pune University Campus, Ganeshkhind, Pune 411 007, India.
email: nabhan@iucaa.ernet.in


Abstract. Recent cosmological observations suggest the existence of a positive cosmological constant Lambda with the magnitude Lambda(G hbar / c3) approx 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

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