Quantum Topology Seminar
Torsten.Asselmeyer-Maluga
German Aerospace Center, Berlin
Spacetime topology at the beginning of the universe
Abstract: In the talk, I will discuss the initial state of the universe at the Big Bang from a topological point of view. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, I will describe the corresponding spacetime as a gravitational instanton. The spatial space is a fractal space (wild embedded 3-sphere) inspired by exotic smoothness in dimension 4. Then, I 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, I’m 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. Here, I found an interesting interpretation of dark matter as knotted worm holes. Then I’m able to determine the initial density of dark matter as the fractal dimension of the Cantor continuum.
See the paper:
https://www.mdpi.com/2073-8994/14/9/1887#
Thursday March 30, 2023 at 12:00 PM in Zoom