Expansional Field Theory: Structural Derivation of the Universal Acceleration from First Principles

This version updates the previous release. Reformatted in two-column layout and corrected multiple technical details. Content updated to match the preprint submission version. Abstract We show that the Expansional Field Theory (EFT), a geometric model in which the universe is represented as a discretized cubic substrate whose expansion defines all effective physical scales, predicts two acceleration scales without introducing new free parameters beyond the observed cosmological timescale t₀. The global acceleration a_ϕᶜosm arises from the fundamental oscillatory mode associated with the cosmological timescale t₀, giving a_ϕᶜosm = c/ (2π t₀). In the presence of condensed matter, the expansion of the substrate is attenuated, defining an effective local rate λₑf. The associated local acceleration a_ϕˡoc follows from the cubic symmetry of the substrate, yielding a_ϕˡoc = (a_ϕᶜosm) /√3. These two quantities form an exact geometric hierarchy (a_ϕᶜosm) / (a_ϕˡoc) = √3, established solely by the geometry of the substrate, without empirical interpolation functions or additional parameters. The predicted values, a_ϕᶜosm ≈ 1. 1×10^ (−10) m/s² and a_ϕˡoc ≈ 6. 3×10^ (−11) m/s², lie within the observed low-acceleration regime of gravitational systems. EFT thus provides a geometric origin for the universal acceleration scale and a testable prediction for a minimum local acceleration, offering a new structural link between cosmological expansion and dynamics in weak-gravity environments.