On topological restrictions of the spacetime in cosmology
T. Asselmeyer-Maluga, J. Krol
TL;DR
This paper explores how differential topology imposes restrictions on the possible shapes and structures of spacetime in cosmology, ruling out certain models like the Poincare dodecahedral space.
Contribution
It applies differential topology to cosmological models, identifying which topologies are compatible with smooth cosmic evolution.
Findings
Poincare dodecahedral model is ruled out
Picard horn topology is ruled out
Sum of two Poincare spheres is allowed
Abstract
In this paper we discuss the restrictions of the spacetime for the standard model of cosmology by using results of the differential topology of 3- and 4-manifolds. The smoothness of the cosmic evolution is the strongest restriction. The Poincare model (dodecaeder model), the Picard horn and the 3-torus are ruled out by the restrictions but a sum of two Poincare spheres is allowed.
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