Relativistic Bitemporal Cosmology in Covariant Bitemporal Geometrodynamics: The Pre-Bounce Σ₄ Throat, Parameter-Free CMB Power Spectrum (A_s = Φ_∞² / 8π), Acoustic Peak Baryon Amplification, 0.302° Cosmic Birefringence, and the 234.8 Gyr Cyclic Unive

Foundational Monograph Series in Covariant Bitemporal Geometrodynamics (CBG) — Paper III (Cosmological Treatise) Standard (3+1)-dimensional ΛCDM cosmology and slow-roll inflation suffer from six foundational breakdowns: the initial Big Bang curvature singularity (a → 0, K₄ → ∞), the Tolman–Penrose Weyl entropy paradox in contracting pre-bounce universes, arbitrary fine-tuning of inflaton potentials to match the Cosmic Microwave Background (CMB) scalar amplitude (A_s ≈ 2.1 × 10⁻⁹), reliance on undetected cold dark matter particles to sustain the third CMB acoustic peak at z_* = 1090, the >5σ Hubble tension (H₀ = 67.4 vs. 73.2 km/s/Mpc) coupled with the 3.5σ DESI dynamical dark energy anomaly (w₀ > −1), and the unexplained 0.30° ± 0.05° isotropic cosmic birefringence rotation in Planck polarimetry. Building upon the variational framework of Covariant Bitemporal Geometrodynamics (CBG) established in Paper I (DOI: 10.5281/zenodo.23443512) and the black hole signature-flip mechanics of Paper II (DOI: 10.5281/zenodo.23451974), we formulate a complete, parameter-free relativistic cosmology on the 5-dimensional manifold M_{3,2} ≃ (ℝ_{t₁} ×_Φ S¹_{t₂}) × Σ₃ governed solely by the universal vacuum topological invariant Φ_∞ = Ω / c = 2.40 × 10⁻⁴ (Ω = 71.95 km/s, Φ_∞² = 5.76 × 10⁻⁸). Specifically, we prove from first principles that: (1) Pre-Bounce Entropy Offloading & BKL Shear Suppression: In the contracting pre-bounce aeon (t₁ < 0), as the cosmological informational saturation scalar approaches unity (σ_cosmo(t₁) = ρ(t₁)/ρ_P → 1), the secondary temporal fiber circumference L_{t₂} = 2π L_P Φ(t₁) expands by 34 orders of magnitude, offloading pre-existing Weyl curvature entropy unitarily from H_{t₁} into Kaluza–Klein winding modes on H_{t₂} and resolving the Tolman–Penrose entropy paradox while preserving Planckian black hole remnants (M_rem = m_P / 2 = 1.088 × 10⁻⁸ kg). (2) Nonsingular Σ₄^{(cosmo)} Quantum Bounce & 703.2 PeV Reheating: Across the Planckian bounce layer (|t₁| ≤ t_P = 5.39 × 10⁻⁴⁴ s), Φ(t₁)² inverts sign and induces a smooth global signature transition (−,−,+,+,+) → (−,+,+,+,+), converting the universe into a nonsingular 4-dimensional spatial throat Σ₄^{(cosmo)} ≃ S¹_w × Σ₃ (a_bounce = 1.978 × 10⁻³²) where Planck fiber stiffness P₀ = c⁷/(ℏG²) halts collapse at ρ_max = ρ_P, bounds the 5D Kretschmann scalar to K₅(0) = 192 / L_P⁴ < ∞, and triggers coherent bitemporal reheating at E_reheat = Φ_∞² E_P = 703.2 PeV (baryon-to-photon ratio η_B = 5.53 × 10⁻¹⁰). (3) Parameter-Free Primordial CMB Power Spectrum: Linearization of the 5D Einstein–Jiménez–Velasco equations yields a modified Mukhanov–Sasaki master equation that derives the exact primordial CMB fluctuation amplitude ΔT/T = Φ_∞ / (4π) = 1.910 × 10⁻⁵, scalar power spectrum A_s = Φ_∞² / (8π) = 2.292 × 10⁻⁹, spectral index n_s = 1 − 2/N_rad = 0.9692 (N_rad = 64.90), and tensor-to-scalar ratio r_{T/S} = 8/N_rad² = 0.00190 without an inflaton field. (4) Baryon-Only Reproduction of the CMB Acoustic Peaks: At recombination (z_* = 1090.3), quadrature coupling between the physical baryon fraction Ω_{b,0} = 0.0493 and the bitemporal acceleration scale a₀^{(CBG)} = 1.20 × 10⁻¹⁰ m/s² yields an effective gravitating matter density Ω_{m,eff}^{(CBG)} = √(2π Ω_{b,0} / 3) = 0.3213 and non-collisional acoustic amplification factor F_CBG = √(2π / 3Ω_{b,0}) − 1 = 5.518 (F_CBG^{(proj)} = 5.435), reproducing the exact CMB acoustic peaks and Doppler troughs (H_{3/2}^{(CBG)} = 0.989) with zero dark matter particles. (5) Exact 0.302° Cosmic Birefringence Holonomy: Parallel transport of CMB polarization vectors across the S¹_{t₂} ↪ M_{3,2} → S²_H bundle from z_* = 1090.3 to z = 0 generates an achromatic Berry–Kaluza–Klein cosmic birefringence rotation of β_CMB^{(CBG)} = Φ_∞ ln(1 + z_*) × 180° = 0.3022° (1,087.9″), matching Planck/WMAP observations and predicting β_reion^{(CBG)}(z_re = 7.7) = 0.0935° for LiteBIRD. (6) DESI Dynamical Dark Energy & the 234.8 Gyr Cyclic Universe: In the late universe, volumetric elastic relaxation of the bitemporal dilaton yields a present-day macroscopic age of t_{1,age} = 14.08 Gyr, resolves the Hubble tension via the local supercluster drift ΔH_local = Ω / R_local = +5.80 km/s/Mpc (H₀ = 67.40 → 73.20 km/s/Mpc), predicts a weakening dark energy equation of state w₀^{(CBG)} = −1 + (2π/3)Ω_{b,0} = −0.897 and w_a^{(CBG)} = −2π Ω_{b,0} = −0.310 consistent with DESI, ends cosmic acceleration at a_decel = 1.862, and proves that cosmic expansion halts at turnaround time t_turn = t_age ln(1/Φ_∞) = 117.4 Gyr (a_max = 64.55), culminating in a perpetual, unitary T_cycle = 234.8 Gyr cyclic universe.