Creating the Universe Without a Singularity and the Cosmological Constant Problem

TL;DR

This paper proposes a non-singular universe origin model using a two-measure theory with a dilaton field, resulting in an effective potential with two flat regions that explain both the universe's beginning and current state, addressing the cosmological constant problem.

Contribution

It introduces a novel two-measure theory framework with a dilaton field that naturally produces a non-singular universe origin and offers insights into the cosmological constant problem.

Findings

Effective potential has two flat regions for different dilaton values.

Avoidance of singularities implies a small positive vacuum energy.

Zero vacuum energy acts as a threshold for universe creation.

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 $\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.