Topological gravity on plumbed V-cobordisms

TL;DR

This paper develops a cosmological model based on generalized BF-theory, where topologically invariant intersection forms of 4D plumbed V-cobordisms determine vacuum coupling constants, linking topology changes to interaction hierarchies.

Contribution

It introduces a novel approach connecting topology of spacetime regions with fundamental interaction constants via intersection forms in a BF-theory framework.

Findings

Calculated rational and integer intersection matrices for topology-changing regions.

Established a relation between matrix element hierarchies and coupling constant hierarchies.

Proposed a topological interpretation of vacuum coupling constants in cosmology.

Abstract

An ensemble of cosmological models based on generalized BF-theory is constructed where the role of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed V-cobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460