Creating the Universe Without a Singularity and the Cosmological Constant Problem

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 $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 $phi rightarrow infty$ 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. This requires a modified emergent universe scenario, where the universe although very old, it does have a beginning.

Using Two Measures Theory to Approach Bags and Confinement

We consider the question of bags and confinement in the framework of a theory which uses two volume elements $sqrt{-{g}}d^{4}x$ and $Phi d^{4}x$, where $Phi $ is a metric independent density. For scale invariance a dilaton field $phi$ is considered. Using the first order formalism, curvature ($Phi R$ and $sqrt{-g}R^{2}$) terms, gauge field term($Phisqrt {- F_{mu u}^{a}, F^{a}_{alphabeta}g^{mualpha}g^{ ubeta}}$ and $sqrt{-g} F_{mu u}^{a}, F^{a}_{alphabeta}g^{mualpha}g^{ ubeta}$) and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags the gauge dynamics is normal, that is non confining, while for the outside, the gauge field dynamics is confining.