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A Topological Signature in Cosmic Topology

G. I. Gomero·M. J. Reboucas·A. F. F. Teixeira
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Abstract

Two procedures for obtaining (extracting and constructing) the topological signature of any multiply connected Robertson-Walker (RW) universe are presented. It is shown through computer-aided simulations that both approaches give rise to the same topological signature for a multiply connected flat RW universe. The strength of these approaches is illustrated by extracting the topological signatures of a flat ($k=0$), an elliptic ($k=1$), and a hyperbolic ($k=-1$) multiply connected RW universes. We also show how separated contributions of the covering isometries add up to form the topological signature of a RW flat universe. There emerges from our theoretical results and simulations that the topological signature arises (in the mean) even when there are just a few images for each object. It is also shown that the mean pair separation histogram technique works, and that it is a suitable approach for studying the topological signatures of RW universes as well as the role of non-translational isometries.

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G. I. Gomero, M. J. Reboucas, A. F. F. Teixeira. 2001-03-30. A Topological Signature in Cosmic Topology. https://doi.org/10.1088/0264-9381%2F18%2F10%2F306

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