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

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 the existence of two universal acceleration quantities with no free parameters. The global acceleration a_ϕ^cosm arises from the fundamental oscillatory mode associated with the cosmological timescale t_0, giving a_ϕ^cosm = c/(2π t_0). In the presence of condensed matter, the expansion of the substrate is attenuated, defining an effective local rate λ_ef. The associated local acceleration a_ϕ^loc follows from the cubic symmetry of the substrate, yielding a_ϕ^loc = (a_ϕ^cosm)/√3. These two quantities form an exact structural hierarchy (a_ϕ^cosm)/(a_ϕ^loc) = √3, established solely by the geometry of the substrate, without empirical interpolation functions or additional parameters. The predicted values, a_ϕ^cosm ≈ 1.1×10^(-10) m/s^2, a_ϕ^loc ≈ 6.3×10^(-11) m/s^2, 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.