Big Bang and Topology

TL;DR

This paper explores the initial universe state at the Big Bang using topology, fractal spaces, and quantum algebra, linking gravitational instantons to topological quantum field theories and quantum symmetries.

Contribution

It introduces a novel approach connecting fractal topology, quantum states, and topological field theories to model the early universe.

Findings

Quantum state derived from fractal space linked to string algebra

Identification of the physical action as the Chern-Simons functional

Quantum symmetry determined as the enveloped Lie algebra U_q(sl_2(C))

Abstract

In this paper we discuss the initial state of the universe at the Big Bang. By using ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as 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 to the Jones polynomial and to Witten's topological field theory. Using this link, we are able to determine the physical theory (action) to be the Chern-Simons functional. The gauge fixing of this action determines the foliation of the spacetime and as well the smoothness properties. Finally, we determine the quantum symmetry of the quantum state to be the enveloped Lie algebra $U_{q}(sl_{2}(\mathbb{C}))$ where $q$ is the 4th root of unity.