A Relativistic Framework of Cosmological Freeze-Out via Spacetime Expansion and Dynamic Void Coupling: Resolving the Baryon Asymmetry Dilemma and Horizon Dualities

The observed Baryon Asymmetry of the Universe (BAU), characterized by the baryon-to-entropy ratio ηB ≈ (6.12 ± 0.04) × 10^-10, remains a prominent challenge in modern cosmology. Standard Model electroweak baryogenesis predicts ηB ∼ 10^-18, falling short of empirical observations by ten orders of magnitude. In this work, we propose a complementary relativistic framework that addresses this discrepancy through macroscopic geometric phase transitions without invoking arbitrary microscopic parameters. Modeling spacetime as a two-component system comprising a visible matter-energy sector (ρE) and a dynamic vacuum potential reservoir (ρV) with negative pressure (PV = -ρV c^2), we show that cosmological dilution naturally triggers an accelerated surge in the Hubble parameter H(t). When the cosmic expansion rate outpaces microscopic annihilation rates (Γ ≪ H), the physical separation velocity between particle pairs exceeds the speed of light via cosmological horizon crossing (D > rH = c/H). This disconnects the null geodesics required for mutual annihilation, inducing a geometric freeze-out within the covariant Boltzmann transport equation. Incorporating a minimal phase divergence in vacuum transition amplitudes, the residual abundance yields ηB ∼ 10^-10\. Furthermore, dynamic coupling resolves the 5σ Hubble tension (H0 ≈ 67.4 km/s/Mpc ↔ 73.0 km/s/Mpc), predicts a scalar spectral index ns ≈ 0.9655, and resolves black hole central singularities (r = 0) via conformal torus geometry (M/Z2). The model predicts a stochastic gravitational wave background peaking in the milli-Hertz band (fpeak ≈ 14 mHz, ΩGW h^2 ≈ 4.2 × 10^-11), strictly complying with Big Bang Nucleosynthesis (BBN) relativistic degree-of-freedom bounds and directly verifiable by the Laser Interferometer Space Antenna (LISA).