The Dark Energy Model in the Priority-Axis Z-Algebra Unified Theory

【Abstract】The standard ΛCDM model reduces dark energy to a constant cosmological term Λ and suffers from two structural shortcomings: it describes only a globally homogeneous repulsive background with no local spatial perturbation degrees of freedom, and dark energy, visible matter and cold dark matter share no unified underlying algebraic origin. Within the priority-axis Z-algebra framework, a two-layer geometric model of dark energy is constructed: the pure B phase (B = span{τ, Ji, Jj, Jk}) forms a static repulsive base layer with B² = +(r² + t²) · 1 + 2zt · χ, while the cross-phase commutator [A, B] = 4t(xi + yj)τ is the unique dynamical carrier. The preferred-axis term 2zt · χ is sealed by a triple algebraic lock at the classical level, yielding an effective equation of state w_eff = −1 + 2K/(K + V) with a decoupling limit w → −1; the three density parameters satisfy the exact normalization Ω_b + Ω_dm + Ω_Λ = 1, with late-time values consistent with Planck 2018. The model closes symmetrically with the dark-matter and gravitational theories of the series. It should be noted that the time-dependent evolution of dark energy described here is at the level of a low-energy effective field theory after projection, and the algebraic necessity of w = −1 remains a heuristic hypothesis awaiting rigorous derivation. Testable predictions include a Quintom-type crossing of w(z) and mild low-redshift deviations confrontable with DESI DR2. All theorem-level statements are verified by an independent exact symbolic-verification script (21 tests, 21 passed, with strictly zero residuals).