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 \(\sqrt{-{g}}d^{4}x\) and \(\Phi d^{4}x\), 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 \(\phi \rightarrow \infty\) relevant for the non singular origin of the Universe and \(\phi \rightarrow -\infty\), describing our present Universe. Surprisingly, avoidance of singularities and stability as \(\phi \rightarrow \infty\) imply a positive but small vacuum energy as \(\phi \rightarrow -\infty\). Zero vacuum energy density for the present universe is the “threshold” for universe creation.