BF systems on graph cobordisms as topological cosmology

TL;DR

This paper develops a topological cosmological model linking universe evolution to graph cobordisms, using BF-type topological field theories to relate invariants to fundamental interaction constants.

Contribution

It introduces a novel topological framework connecting graph cobordisms with cosmological evolution and fundamental constants via BF-models.

Findings

Explicit transition amplitudes for BF-models are derived.

Topological invariants correspond to physical coupling constants.

Eigenvalues of intersection matrices reproduce hierarchy of fundamental interaction constants.

Abstract

A cosmological model connecting the evolution of universe with a sequence of topology changes described by a collection of specific graph cobordisms, is constructed. It is shown that an adequate topological field theory (of BF-type) can be put into relation to each graph cobordism. The explicit expressions for transition amplitudes (partition functions) are written in these BF-models and it is shown that the basic topological invariants of the graph cobordisms (intersection matrices) play the r{\^o}le of coupling constants between the formal analogues of electric and magnetic fluxes quantized {\`a} la Dirac, but with the use of Poicar{\'e}--Lefschetz duality. For a specific graph cobordism, the diagonal elements and eigenvalues of the intersection matrix reproduce the hierarchy of dimensionless low-energy coupling constants of the fundamental interactions acting in the real universe.