The Universe as a Set of Topological Fluids with Hierarchy and Fine Tuning of Coupling Constants in Terms of Graph Manifolds

TL;DR

This paper models the hierarchy and fine tuning of gauge coupling constants in the universe using topological invariants of graph manifolds, linking topological properties to physical constants and proposing a solution to the cosmological constant problem.

Contribution

It introduces a novel topological framework using graph manifolds to explain the hierarchy and fine tuning of gauge coupling constants in physics.

Findings

Hierarchy of coupling constants modeled by linking matrices.

Specific graph manifolds replicate the universe's coupling hierarchy.

Proposed a topological solution to the cosmological constant fine tuning problem.

Abstract

The hierarchy and fine tuning of the gauge coupling constants are described on the base of topological invariants (Chern classes interpreted as filling factors) characterizing a collection of fractional topological fluids emerging from three dimensional graph manifolds, which play the role of internal spaces in the Kaluza-Klein approach to the topological BF theory. The hierarchy of BF gauge coupling constants is simulated by diagonal elements and eigenvalues of rational linking matrices of tree graph manifolds pasted together from Brieskorn (Seifert fibered) homology spheres. Specific examples of graph manifolds are presented which contain in their linking matrices the hierarchy of coupling constants distinctive for the dimensionless coupling constants in our Universe. The fine tuning effect is simulated owing to the special numerical properties of diagonal elements of the linking matrices. We pay a particular attention to fine tuning problem for the cosmological constant and propose its model solution.