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

Uma nova etapa da Instrução Normativa n° 51: a Região Centro-Sul.

Após a verificação da insuficiente qualidade do leite produzido no País, a Secretaria de Defesa Agropecuária (SDA/Mapa) publicou a Instrução Normativa nº 51 em setembro de 2002 (IN nº 51/2002), cujas novas exigências entraram em vigor, na Região Centro-Sul, em 1º/7/2005. Esse normativo estabelece requisitos mínimos de qualidade para os leites tipo A, B e C, para o leite cru refrigerado e pasteurizado, além de dispor normas para a coleta a granel da matériaprima. Para as regiões Norte e Nordeste, essas exigências só passarão a ser obrigatórias a partir de 1º/7/2007. Trata-se de uma iniciativa que deverá incentivar a melhoria da qualidade do leite inspecionado por meio da aplicação de testes de qualidade mais rigorosos. Estão previstas, com base em um calendário diferenciado por região, etapas progressivas para a melhoria da qualidade, as quais se estendem de 2002 a 2011 para a Região Centro-Sul (Sul, Sudeste e Centro-Oeste), e de 2002 a 2012 para as regiões Norte e Nordeste. A pequena produção leiteira deverá adequar-se às novas disposições normativas mediante a sua organização em associações, bem como com a disponibilização de tanques comunitários de resfriamento

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

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