A $T_0$-discrete universe model with five low-energy fundamental interactions and the coupling constants hierarchy

Abstract

A quantum model of universe is constructed in which values of dimensionless coupling constants of the fundamental interactions (including the cosmological constant) are determined via certain topological invariants of manifolds forming finite ensembles of 3D Seifert fibrations. The characteristic values of the coupling constants are explicitly calculated as the set of rational numbers (up to the factor $2π$) on the basis of a hypothesis that these values are proportional to the mean relative fluctuations of discrete volumes of manifolds in these ensembles. The discrete volumes are calculated using the standard Alexandroff procedure of constructing $T_0$-discrete spaces realized as nerves corresponding to characteristic canonical triangulations which are compatible with the Milnor representation of Seifert fibered homology spheres being the building material of all used 3D manifolds. Moreover, the determination of all involved homology spheres is based on the first nine prime numbers ($p_1=2, >..., p_9=23$). The obtained hierarchy of coupling constants at the present evolution stage of universe well reproduces the actual hierarchy of the experimentally observed dimensionless low-energy coupling constants.