TY - JOUR

T1 - Connecting the nonsingular origin of the universe, the vacuum structure and the cosmological constant problem

AU - Guendelman, Eduardo I.

AU - Labraña, Pedro

N1 - Funding Information:
their wonderful hospitality. P. L. has been partially supported by FONDECYT grant N0 11090410, Mecesup UBB0704 and Universidad del Bío-Bío through grant DIUBB 121407 GI/VC.

PY - 2013/7/1

Y1 - 2013/7/1

N2 - We consider a nonsingular 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 Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field φ 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 (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial 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 φ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and φ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial 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 φ → -∞, 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 nontrivial 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.

AB - We consider a nonsingular 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 Φd4x, where Φ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field φ 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 (SSB) of scale invariance (SI). After SSB of SI, it is found that a nontrivial 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 φ → ∞ relevant for the nonsingular origin of the universe, followed by an inflationary phase and φ → -∞, describing our present universe. The dynamics of the scalar field becomes nonlinear and these nonlinearities produce a nontrivial 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 φ → -∞, 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 nontrivial 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.

KW - Cosmological constant problem

KW - emergent universe

KW - nonsingular cosmology

KW - scale invariance

KW - two measures theory

UR - http://www.scopus.com/inward/record.url?scp=84878924604&partnerID=8YFLogxK

U2 - 10.1142/S0218271813300188

DO - 10.1142/S0218271813300188

M3 - Review article

AN - SCOPUS:84878924604

SN - 0218-2718

VL - 22

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

IS - 9

M1 - 1330018

ER -