NONSINGULAR ORIGIN OF THE UNIVERSE AND THE COSMOLOGICAL CONSTANT PROBLEM

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 root-gd(4)x and Phi d(4)x, where Phi is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field phi 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 phi -> infinity relevant for the nonsingular origin of the universe and phi -> -infinity, describing our present universe. Surprisingly, avoidance of singularities and stability as phi -> infinity imply a positive but small vacuum energy as phi -> -infinity. Zero vacuum energy density for the present universe is the " threshold" for universe creation.