Cosmological BF Theory on Topological Graph Manifold with Seifert Fibered Homology Spheres

Abstract

In this article, we show how to build a cosmological model characterized by the hierarchy of coupling constants and a set of Quantum Hall Fluids in BF theory. The resulting field theory is operated on Abelian Gauge fields within Gauge transformations on the ( ) 1 U group, which introduces the Chern-Simmons class with topological mass. The mathematical background on which the model is based is a topological graph manifold of Brieskorn Seifert fibered-sphere space-time grid (lower dimensions), through a Kaluza-Klein reduction. This model offers a feasible alternative to the precise calculation of the cosmological constant Λ, much more accurate than the string landscape and baby universe models that have been proposed. Numerical results are given for coupling constants hierarchy. Model predictions may work as an argumental base to justify topological interpretations of space-time.