Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-02-27
Phys.Lett.A311:319-330,2003
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, 1 figure, latex2e. New references added. Inserted clarifying points. To appear in Phys. Lett. A (2003) in the presen
Scientific paper
10.1016/S0375-9601(03)00540-1
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We first give a complete description of the diffeomorphic classification of compact flat 3-manifolds, and derive the expressions for the injectivity radii, and for the volume of each class of Euclidean 3-manifolds. There emerges from our calculations the undetectability conditions for each (topological) class of flat universes. To illustrate the detectability of flat topologies we construct toy models by using an assumption by Bernshtein and Shvartsman which permits to establish a relation between topological typical lengths to the dynamics of flat models.
Gomero G. I.
Reboucas Marcelo J.
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