Detectability of Cosmic Topology in Flat Universes
Abstract
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.
Keywords
Cite
@article{arxiv.gr-qc/0202094,
title = {Detectability of Cosmic Topology in Flat Universes},
author = {G. I. Gomero and M. J. Reboucas},
journal= {arXiv preprint arXiv:gr-qc/0202094},
year = {2009}
}
Comments
17 pages, 1 figure, latex2e. New references added. Inserted clarifying points. To appear in Phys. Lett. A (2003) in the present form