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

TL;DR

This paper investigates the topological signatures in cosmic crystallography, focusing on Euclidean isometries and how they manifest in pair separation histograms to identify universe topology.

Contribution

It introduces methods to distinguish topological from statistical spikes in pair separation histograms and explores signatures of non-translational isometries in small Euclidean universes.

Findings

Topological spikes alone cannot distinguish manifolds with the same Clifford translations.

Mean pair separation histograms help reduce noise and identify topological features.

Non-translational isometries also produce detectable topological signatures.

Abstract

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.