nLab cosmic topology





topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory


Basic concepts

Universal constructions

Extra stuff, structure, properties


Basic statements


Analysis Theorems

topological homotopy theory



In cosmology, by cosmic topology one refers to (the possibility, or possible detection of) non-trivial global topology of the spacetime manifold which is the cosmos, hence its (possible) non-homeomorphy to the Cartesian space with its Euclidean topology which is underlying Minkowski spacetime.

Cosmic topology is usually understood to refer to the universe at large only: for instance any non-trivial topology of black hole spacetimes (due to being defined only on the complement spacetime of their would-be singularity, cf. singular brane) is not of concern in discussions of cosmic topology.

For example, in a simple scenario of cosmic topology, space at large might be homeomorphic to a 3-torus of large (huge) radii (which could in principle be detected by showing that images of galaxies repeat periodically in certain directions) or to a 3-sphere (cf. here), or to a lens space [URLW 2004, ALS 2005, Aurich & Lustig 2012a, 2012b], which might be detectable by cose analysis of the cosmic microwave background.

Implications on cosmic electromagnetism

Of particular interest for cosmic electromagnetism would be non-simply-connected cosmic topologies (such as the 3-torus or a lens space but not the 3-sphere) since these could support locally trivial but globally non-trivial electromagnetic fields (namely with vanishing electromagnetic flux density but still non-trivial holonomy/monodromy around non-conctracticle cosmological curves) such as discussed in the Aharonov-Bohm effect.

Moreover, lens space-topology with its integral torsion-cohomology group in degree 2 (cf. there) would even support “fractional” such electromagnetic fields (for which certain integer multiples of the field would vanish), which would in principle be detectable by an uncertainty principle for quantum observables on the cosmic electromagnetic field [Freed, Moore & Segal 2007b, p. 28].


See also:

Analysis in the generality of inhomogeneous cosmology:

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Last revised on June 7, 2024 at 13:39:29. See the history of this page for a list of all contributions to it.