Spherical VS Flat Spatial Sections in Cosmology

Abstract

The global geometry of space is an open question in Cosmology. We study models of spatially spherical and flat Universes, that tunnel from a state of no classical spacetime into an asymptotically deSitter spacetime. Motivated by the Horizon Problem, we propose that our Universe be created with an initial length scale of 100L_p and that a pre-inflationary era is required for a sufficiently homogeneous space before Inflation. It is found that for a spherical Universe, favourable conditions to solve the Horizon Problem may be achieved by considering a Universe dominated with dark energy or cosmic strings. For a flat and compact Universe, we find that the Null Energy Condition (NRC) have to be violated in order to avoid an initial singularity. An inclusion of an NRC-violating scalar field results in a spacetime free of singularities and satisfies the requirements for a smooth and homogeneous Universe to evolve.