Evolution of the Fine Structure Constant as a Consequence of Stochastic Geometrodynamics of Phase Defects in a Four_Dimensional Timelike Manifold

Within an alternative approach to the unification of interactions on a dynamical manifold M4(x, y, z, w) with a timelike coordinate w, a theoretical mechanism for the cosmological “running” of dimensionless coupling constants is proposed. It is shown that the effective vacuum permittivity εeff , induced by the correlator of the density of topological phase defects (vortex lines), depends rigidly on the metric tensor gww. A procedure of stochastic averaging of the field equations in the second order of perturbation theory is carried out following the Zeldovich–Kamenev methodology. A scaling dependence of the macroscopic coupling parameter β(z) ∝ (1 + z)^1.2 is derived on the basis of the Kibble–Zurek scenario and the running self-coupling constant of the scalar field λ(z), using the critical indices of three-dimensional Ginzburg–Landau phase singularities (α ≈ 0.6). The key element of the derivation is the postulate that the longitudinal correlation length along w is fixed by the baryon Compton wavelength. A spatiotemporal variation of the observed fine structure constant αeff (z) in the early Universe (z ∼ 7–9) is predicted, bounded by local geometric screening. A testable prediction for the 21-cm line at z ∼ 15–20 is discussed. In the outlook, a possible connection between topological ruptures of the 3D fabric and the nature of white holes is noted.