Geometric Baryogenesis: Chiral Anomaly and Matter-Antimatter Asymmetry in the Zhang Effective Metric

The observed dominance of matter over antimatter in the universe remains one of the most profound unresolved problems in cosmology. The Standard Model fails to produce the required baryon asymmetry due to insufficient CP violation. In this paper, we propose a geometric mechanism for baryogenesis within the rotational-order geometric unification framework. Using the Zhang Effective Metric, we demonstrate that the early-universe phase transition of the internal S³ orientation field violates CP symmetry through geometric chiral anomalies. The time-varying gradient of the internal space dynamically generates a chiral chemical potential, while topological transitions (sphalerons) and rapid non-adiabatic evolution satisfy all three Sakharov conditions. We show that this geometric process naturally generates the observed baryon-to-photon ratio (~6×10⁻¹⁰) at a temperature T ~ 10⁹ GeV, without requiring new scalar fields or explicit CP-violating phases.