Cosmological constant - the weight of the vacuum

Recent cosmological observations suggest the existence of a positive cosmological constant A with the magnitude Lambda(Gh/c(3))approximate to10(-123). This review discusses several aspects of the cosmological constant both from the cosmological (Sections 1-6) and field theoretical (Sections 7-11) perspectives. After a brief introduction to the key issues related to cosmological constant and a historical overview, a summary of the kinematics and dynamics of the standard Friedmann model of the universe is provided. The observational evidence for cosmological constant, especially from the supernova results, and the constraints from the age of the universe, structure formation, Cosmic Microwave Background Radiation (CMBR) anisotropies and a few others are described in detail, followed by a discussion of the theoretical models (quintessence, tachyonic scalar field,...) from different perspectives. The latter part of the review (Sections 7-11) concentrates on more conceptual and fundamental aspects of the cosmological constant like some alternative interpretations of the cosmological constant, relaxation mechanisms to reduce the cosmological constant to the currently observed value, the geometrical structure of the de Sitter spacetime, thermodynamics of the de Sitter universe and the role of string theory in the cosmological constant problem. (C) 2003 Elsevier Science B.V. All rights reserved.