Spikes in Cosmic Crystallography II: Topological Signature of Compact Flat Universes

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

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15 pages, 5 figures, LaTeX2e; Added 2 references and inserted clarifying details. To appear in Phys. Lett. A (2000) in the pre

Scientific paper

10.1016/S0375-9601(00)00606-X

We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of individual PSH's using mean pair separations histograms we show how to distinguish between topological and statistical spikes. We report results of simulations that evince that topological spikes are not enough to distinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSH's corresponding to euclidean small universes. We also show how to evince the topological signature due to non-translational isometries.

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