
TL;DR
This review discusses the theoretical and observational aspects of cosmic topology, exploring possible multi-connected universe models, their signatures, and current evidence, including methods like cosmic crystallography and Bayesian analysis.
Contribution
It provides a comprehensive overview of the topological concepts, candidate models, and detection methods for cosmic topology, highlighting recent observational constraints from Planck data.
Findings
No conclusive evidence of multi-connected topology from recent observations
Exploration of candidate topologies like Poincare Dodecahedron and Bianchi Universes
Discussion of methods for detecting cosmic topology, including circles in the sky and Bayesian analysis
Abstract
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant of local curvature, Einstein's equations of relativity do not constrain the global properties of space-time. The topological requirements of a universal space time manifold are discussed, including requirements of space-time orientability and causality. The basic topological concepts used in classification of spaces, i.e. the concept of the Fundamental Domain and Universal covering spaces are discussed briefly. The manifold properties and symmetry groups for three dimensional manifolds of constant curvature for negative, positive and zero curvature manifolds are laid out. Multi-connectedness is explored as a possible explanation for the detected…
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Taxonomy
TopicsCosmology and Gravitation Theories · Advanced Mathematical Theories and Applications · Relativity and Gravitational Theory
