Connecting The Non-Singular Origin of the Universe, The Vacuum Structure and The Cosmological Constant Problem

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 produce a non trivial vacuum structure for the theory and are responsible for 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. The non trivial vacuum structure is crucial to ensure the smooth transition from the emerging phase, to an inflationary phase and finally to the slowly accelerated universe now. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.

44 pages, 5 figures. Typos corrected, two new figures, references added. Invited review to be published in IJMPD

References in corpus (5)

• Dark energy from modified gravity with Lagrange multipliers
• 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
• Observational constraints on a cosmological model with Lagrange multipliers
• Dynamical Couplings, Dynamical Vacuum Energy and Confinement/Deconfinement from R^2-Gravity
• A Way to Dynamically Overcome the Cosmological Constant Problem

Cited by in corpus (18)

• Stability of the Einstein static Universe in $f(R,T)$ gravity
• Unification of inflation and dark energy {\it à la} quintessential inflation
• Emergent Cosmology, Inflation and Dark Energy
• One Hundred Years of the Cosmological Constant: from 'Superfluous Stunt' to Dark Energy
• Two scalar fields inflation from scale-invariant gravity with modified measure
• Emergent universe scenario and the low CMB multipoles
• Unifying Inflation with early and late Dark Energy in Multi-Fields: Spontaneously broken scale invariant TMT
• Curvaton reheating in a Scale Invariant Two Measures Theory
• Instant preheating in a scale invariant two measures theory
• Emergent Universe by Tunneling in a Jordan-Brans-Dicke Theory
• Cosmology from multimeasure multifield model
• Classically and Quantum stable Emergent Universe from Conservation Laws
• Einstein's Field Equations as a Fold Bifurcation
• Cosmological Solutions from a Multi-Measure Model with Inflaton Field
• The multi-measure cosmological model and its peculiar effective potential
• Special cases of the Multi-Measure Model -- understanding the prolonged inflation
• Cosmological solutions from models with unified dark energy and dark matter and with inflaton field
• The role of the slope in the the multi-measure cosmological model