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.
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