Non Singular Origin of the Universe and the Cosmological Constant Problem (CCP)

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 $\sqrt{-g}{d}^{4}x$ and $\mathrm{\Phi }{d}^{4}x$, where $\mathrm{\Phi }$ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field $\varphi$ 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 $\varphi \to \mathrm{\infty }$ relevant for the non singular origin of the Universe and $\varphi \to -\mathrm{\infty }$, describing our present Universe. Surprisingly, avoidance of singularities and stability as $\phi \rightarrow \infty$implyapositivebutsmallvacuumenergyas$\phi \rightarrow -\infty$. Zero vacuum energy density for the present universe is the “threshold” for universe creation.