Concomitant Projection Mechanism and the Geometric Origin of Accelerating Cosmic Expansion

We present a geometric mechanism for the accelerating expansion of the universe that requires no dark energy component. In the META Physics framework (Multi-dimensional Emergence Theory of Actuality), a uniformly rotating four-dimensional ball B⁴ (R) with two independent angular velocities (Ω₁, Ω₂) serves as the Projection System. An observer anchored on the boundary three-sphere S³ (R) experiences a concomitant projection Πcon = Pₐ ∘ Fₐ, consisting of a co-rotating frame transformation followed by a tangent-space projection. This projection reverses the sign of the centripetal acceleration (−ω² → +ω²), converting harmonic oscillation into de Sitter expansion with effective cosmological constant Λₑff = 3Ω̄², where Ω̄ = (Ω₁ + Ω₂) /2. Three core results are established: (1) Sign reversal and de Sitter expansion. The concomitant projection converts restoring force into repulsive force. The effective cosmological constant Λₑff = 3Ω̄² = 3/R² is confirmed independently through the O'Neill A-tensor of the Hopf submersion, establishing Ω̄ = 1/R with zero additional assumptions. The universal coefficient 3 in the O'Neill formula is traced to its combinatorial origin in the vertical cross-terms of the Riemann curvature expansion. (2) Uniqueness of the concomitant projection. The projection Πcon, identified with the Hopf fibration S³ → S², is proven unique via a triple-lock proof from three independent mathematical disciplines: Escobales' classification theorem (Riemannian geometry), Reeb flow uniqueness (contact dynamics), and the algebraic structure of the U (1) quotient (complex algebraic geometry). Even if any single lock is invalidated, the remaining two guarantee uniqueness. (3) Acceleration oscillation, permanent acceleration, and observational consistency. When Ω₁ ≠ Ω₂, beating between the two independent rotation planes produces acceleration oscillation with frequency ωₒsc = 2δΩ. The effective equation of state w (z) = −1 + A·cosφ₀ − k·ln (1+z) oscillates logarithmically in redshift space. The deceleration parameter satisfies q (t) 0 under δΩ/Ω̄ < √2 (permanent acceleration theorem): no deceleration epoch exists, and the observed transition is reinterpreted as alternation between strong and weak acceleration. These predictions are consistent with DESI DR2 BAO data (2. 8σ–4. 2σ against ΛCDM). The phantom crossing reported in CPL analyses is reinterpreted as a phase transition in the geometric oscillation, requiring no violation of the Null Energy Condition. An independent determination of Ω̄ from the electron mass formula mₑ = α⁻¹⁸ ℏΩ̄/c² yields a zero-free-parameter prediction H₀ = 67. 84 km/s/Mpc (Planck +0. 9σ). The inputs are two particle-physics constants (α, mₑ) and the age of the universe (t₀) — no cosmological fitting parameters. If the acceleration oscillation is physical, the standard assumption of a monotonically varying H (z) underlying both CMB-based and local H₀ inferences may require revision, providing a structural context for the Hubble tension. v2. 0 applies the META Physics preprint series standard (STYLE v2. 0): Author block updated, Glossary and Colophon added, Series and Companion papers registered, Established Results inline system applied, internal document references replaced with companion paper citations, Discussion section restructured, English harmonized with PP-07–09.