Geometric Relaxation Cosmology: Unified Theory of Dark Components

Geometric Relaxation Cosmology (GRC) presents a fundamental theory unifying dark matter and dark energy through a geometric framework. The cosmological state is described by a point on S² with angles θ and φ determining densities through: Ω_dm = cos²θ, Ω_b = sin²θ cos²φ, Ω_Λ = sin²θ sin²φ. **Key features:** • Geometric derivation from string compactification • Four parameters: θ_eq=59.05°, φ_eq=75.00°, τ_θ=5.99 Gyr, τ_φ=7.92 Gyr • Three testable predictions distinct from ΛCDM: 1. w(z) = -0.9815 + 0.0175z/(1+z) (Euclid, 5.2σ) 2. f_iso = 0.025 ± 0.008 (CMB-S4, 5σ) 3. Δα/α = -1.1×10⁻¹⁸ yr⁻¹ (atomic clocks, 5σ by 2030)