Big Bang and Topology

In this paper, we discuss the initial state of the universe at the Big Bang. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as a gravitational instanton. The spatial space is a fractal space (wild embedded 3-sphere)....

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 14; no. 9; p. 1887
Main Authors: Asselmeyer-Maluga, Torsten, Król, Jerzy, Wilms, Alissa
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.09.2022
Subjects:
Big bang cosmology
Embedding
Field theory
Fractals
Instantons
Lie groups
Polynomials
Quantum field theory
Relativity
Smoothness
Spacetime
Theory of relativity
Topology
Universe
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:In this paper, we discuss the initial state of the universe at the Big Bang. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as a gravitational instanton. The spatial space is a fractal space (wild embedded 3-sphere). Then, we construct the quantum state from this fractal space. This quantum state is part of the string algebra of Ocneanu. There is a link between the Jones polynomial and Witten’s topological field theory. Using this link, we are able to determine the physical theory (action) as the Chern–Simons functional. The gauge fixing of this action determines the foliation of the spacetime and the smoothness properties. Finally, we determine the quantum symmetry of the quantum state to be the enveloped Lie algebra Uq(sl2(C)), where q is the fourth root of unity.
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content type line 14
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14091887