Abstract The unification of fundamental interactions and the nature of dark energy remain two of the most profound challenges in modern theoretical physics. Most existing unified field approaches rely on external symmetries or high-dimensional extensions, while dark energy is often treated as a static cosmological constant or a scalar field with ad hoc potentials. As the third volume of the 14FT Unified Field Theory under the Order Variation Theory, this work presents a modified generally covariant 14FT unified field equation, which incorporates an internal complementary duality drive term (\ (₂₃\) ) dynamically determined by three dimensionless state variables: the degree of duality channel completeness (\ (n\) ), the phase alignment angle (\ (\) ), and the unreleased topological potential (\ (UT\) ). The proposed equation naturally reduces to general relativity in the weak-field and low-velocity limit, providing a self-consistent dynamical interpretation of dark energy as an emergent structural drive rather than a fundamental constant. We verify four key limiting cases to validate the framework’s consistency, including the regimes of missing duality, perfect duality, Newtonian approximation, and vacuum cosmology. Additionally, we present a minimal set of evolution equations that describe the time-dependent behavior of the duality state variables, forming a closed dynamical system. This framework, as the third volume of the 14FT Unified Field Theory under the Order Variation Theory, offers a novel perspective on cosmic evolution, suggesting that the universe evolves toward higher-duality states, and provides a testable model for the dynamical evolution of dark energy. The mathematical structure of the theory is self-contained and does not depend on specific physical interpretations of the duality variables, making it suitable for further mathematical refinement and cosmological observational tests. The 14FT geometric basis of the unified field equation also aligns with the symmetry principles underlying fundamental interactions, providing a new geometric perspective for unification 2.
Liukun Wen (Wed,) studied this question.