Sahni, VarunStarobinsky, A. A.2012-03-122012-03-122000-04-25http://hdl.handle.net/11007/1256Recent observations of Type 1a supernovae indicating an accelerat- ing universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmolog- ical tests of Λ 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 Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects – mechanisms which are known to give rise to a large value of Λ hence leading to the ‘cosmological constant problem’. More recent at- tempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modeling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.enFRW Cosmological models with Λ = 0Observational consequences of a cosmological Λ-termPositive Cosmological Λ-termPreprint