NONSINGULAR ORIGIN OF THE UNIVERSE AND THE COSMOLOGICAL CONSTANT PROBLEM

Abstract

We consider a nonsingular origin for the universe starting from an Einstein static universe in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field ϕ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe and ϕ → -∞, describing our present universe. Surprisingly, avoidance of singularities and stability as ϕ → ∞ imply a positive but small vacuum energy as ϕ → -∞. Zero vacuum energy density for the present universe is the "threshold" for universe creation.