Non Singular Origin of the Universe and its Present Vacuum Energy Density

Abstract

We consider a non singular origin for the Universe starting from an Einstein static Universe, the so called "emergent universe" scenario, 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, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field $\varphi$ are considered in the action. The first order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of scale invariance (S.I.). After S.S.B. of S.I., it is found that a non trivial potential for the dilaton is generated. 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 $\varphi \to \infty$ relevant for the non singular origin of the Universe, followed by an inflationary phase and $\varphi \to -\infty$, describing our present Universe. The dynamics of the scalar field becomes non linear and these non linearities are instrumental in the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in $\varphi \to -\infty$, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

28 pages, short version of this paper awarded an honorable mention by the Gravity Research Foundation, 2011, accepted for publication in International Journal of Modern Physics A

References in corpus (6)

• Emergent Universe with Exotic Matter
• Fine Tuning Free Paradigm of Two Measures Theory: K-Essence, Absence of Initial Singularity of the Curvature and Inflation with Graceful Exit to Zero Cosmological Constant State
• Absence of the Fifth Force Problem in a Model with Spontaneously Broken Dilatation Symmetry
• Transition to Zero Cosmological Constant and Phantom Dark Energy as Solutions Involving Change of Orientation of Space-Time Manifold
• Bags and Confinement Governed by S.S.B. of Scale Invariance
• A Way to Dynamically Overcome the Cosmological Constant Problem

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• Emergent Universe by Tunneling
• Unified Dark Energy-Dark Matter model with Inverse Quintessence
• Emergent Universe by Tunneling in a Jordan-Brans-Dicke Theory
• Non Singular Origin of the Universe and the Cosmological Constant Problem (CCP)
• The nucleation of false vacuum bubbles with compact geometries