The Status of Cosmic Topology after Planck Data

TL;DR

Recent astronomical data from WMAP and Planck have made testing the universe's shape feasible, with current observations supporting simple models but also allowing for complex topologies like multi-connected spaces.

Contribution

This paper reviews the theoretical developments and observational constraints on cosmic topology following recent Planck data, highlighting the compatibility of complex topologies with current observations.

Findings

Planck data supports a flat, infinite universe model

Complex topologies like Poincare Dodecahedral Space remain consistent with observations

No definitive evidence for a finite, multi-connected universe has been found

Abstract

In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply-connected or multi-connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi-connected small universe models is to create multiples images of faraway cosmic sources. While the last CMB (Planck) data fit well the simplest model of a zero-curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincare Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. We review the theoretical and observational status of the field.