A Topological Signature in Cosmic Topology

Details A Topological Signature in Cosmic Topology A Topological Signature in Cosmic Topology

1999-11-13

arxiv.org/abs/gr-qc/9911049v2

Class.Quant.Grav. 18 (2001) 1885-1906

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 7 figures, LaTeX2e. Inserted: clarifying details, a connection with CCP method, new references. To appear in Class.

Scientific paper

10.1088/0264-9381/18/10/306

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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