Topological Lensing in Spherical Spaces

TL;DR

This paper classifies all 3D spherical manifolds and evaluates their detectability in cosmology using crystallographic methods, predicting pair separation histograms and confirming stability through simulations.

Contribution

It provides a complete classification of spherical 3D manifolds and assesses their observability via cosmic object catalogs and pair separation histograms.

Findings

Complete classification of spherical 3D manifolds.

Predicted pair separation histogram features.

Method stability confirmed by simulations.

Abstract

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogs of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.