Exploring the global topology of the universe

In this talk work done by our group on cosmic topology is reviewed. It ranges from early attempts to solve a famous controversy about quasars through the multiplicity of images, to quantum cosmology in this context and an application to QED renormalization.Comment: 4 pages. Contribution to the XXII Brazilian National Meeting on Particles and Fields, Sao Lourenco, October 200

Cosmic Crystallography with a Pullback

We present a modified version of the cosmic crystallography method, especially useful for testing closed models of negative spatial curvature. The images of clusters of galaxies in simulated catalogs are ``pulled back'' to the fundamental domain before the set of distances is calculated.Comment: 9 pages, 2 figure

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