Dynamical Evolution of Dark Energy in the Zhang Effective Metric: A Geometric Model for DESI Dark Energy Constraints

The ΛCDM cosmological model treats dark energy as a cosmological constant with w = -1. Recent data from DESI DR2 exhibits tentative preference for a redshift-evolving dark energy equation of state that may cross the phantom divide w < -1. Within the rotational-order geometric unification framework, the Zhang Effective Metric supports slow relaxation of the internal S³ orientation field on cosmological scales. This geometric relaxation produces an effective dynamical dark energy component. We derive the redshift-dependent w(z) relation and demonstrate that the predicted evolution matches the tentative trend from DESI full-shape and BAO measurements. Unlike phenomenological models with arbitrary fitting parameters, the evolution of w(z) is controlled by the internal fibre topology of the framework. The Hubble parameter H(z) predicted by this geometric model offers a distinct falsifiable signature for upcoming cosmological surveys.