Non singular origin of the universe and its connection to the cosmological constant problem (CCP)

Abstract

We consider a non singular origin for the Universe starting from an Einstein static Universe in the framework of a theory which uses two volume elements sqrt −gd 4 x and ϕd 4 x, 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 non singular 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.