Closed Spaces in Cosmology

This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a 3-dimensional, closed Riemannian manifold. The discussed topics are: (1) A comparison, previously obtained, between Thurston's geometries and Bianchi-Kantowski-Sachs metrics for such 3-manifolds is here clarified and developed. (2) Some implications of global inhomogeneity for locally homogeneous 3-spaces of constant curvature are analyzed from an observational viewpoint.Comment: 20 pages, 6 figures, revised version of published paper. In version 2: several misprints corrected, 'redshifting' in figures improved. Version 3: a few style corrections; couple of paragraphs in subsection 2.4 rewritten. Version 4: figures 5 and 6 corrrecte

Birth of a Closed Universe of Negative Spatial Curvature

We propose a modified form of the spontaneous birth of the universe by quantum tunneling. It proceeds through topology change and inflation, to eventually become a universe with closed spatial sections of negative curvature and nontrivial global topology.Comment: 10 pages, 1 figure. Revised version with better comments on assumed topology chang

Some integrals ocurring in a topology change problem

In a paper presented a few years ago, De Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes (Phys. Rev. D 56, 3329 (1997)). The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space).Comment: RevTeX article, 4 pages, 1 figur

An Infinite Number of Closed FLRW Universes for Any Value of the Spatial Curvature

The Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply connected; they have finite volume in the positive curvature case, and infinite volume in the null and negative curvature ones. I want to call the attention to the existence of an infinite number of models, which are based on these same metrics, but have compact, finite volume, multiply connected spatial sections. Some observational implications are briefly mentioned.Comment: 4 pages. Contribution to the 5th International Workshop on Astronomy and Relativistic Astrophysics (Joao Pessoa, PB, Brazil, October 10-12, 2011) and to the 1o. Simposio Jayme Tiomno (Brasilia, DF, Brazil, October 27-28, 2011). In version 2: a few minor corrections; two new references added. In this version: title correction in Ref. 3; dedication paragraph at the en

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with compact spatial sections of negative spatial curvature.Comment: 10 pages. Contribution to the "Fifth Alexander Friedmann International Seminar on Gravitation and Cosmology," Joao Pessoa, Brazil, 2002. Revised version, with altered Abstract and one new referenc