The Shape and Topology of the Universe
Jean-Pierre Luminet
TL;DR
This paper reviews how tessellations help model the universe's shape and discusses the dodecahedral space hypothesis as an explanation for cosmic microwave background anomalies.
Contribution
It introduces tessellations as a method to construct multiply-connected universe models and explores the dodecahedral space proposal for explaining CMB features.
Findings
Tessellations are useful for modeling universe topology.
The dodecahedral space model may explain CMB anomalies.
Finite, positively curved universe models are plausible.
Abstract
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces useful for cosmology. We discuss more particularly the proposal of a finite, positively curved, dodecahedral space for explaining some puzzling features of the cosmic microwave background radiation, as revealed by the 2003-2006 WMAP data releases.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Cosmology and Gravitation Theories · Digital Image Processing Techniques