Cosmological Expansion from Temporal Kinetics in the Scalar Temporal Field Ontology

The Scalar Temporal Field Ontology (STFO) models time as a dynamical scalar field whose spacetime gradients generate causal structure, inertia, and temporal directionality. This work derives the exact, model-independent relationship between the cosmological expansion rate and the temporal kinetic amplitude on homogeneous and isotropic backgrounds. We show that the Hubble parameter is both a geometric measure of temporal congruence divergence and an algebraic function of the temporal kinetic sector through the Friedmann equations. Cosmological expansion is thereby reinterpreted as a dynamical manifestation of temporal flow, fixing the physical meaning of the Hubble parameter within the STFO framework.