The TVVVV Framework of the Dark Sector: Dynamical Torsion, Open Quantum Geometry, and Emergent Cosmological Response

This work presents a rigorous canonical and perturbative analysis of the TVVVV cosmological framework, an effective field theory featuring a dynamical first-order tetrad-spin connection theory with dynamical spacetime torsion (D_σ T D^σ T). Using the Dirac-Bergmann constraint algorithm, the theory is confirmed as a degenerate higher-derivative system that avoids generic Ostrogradsky instabilities, yielding exactly five physical degrees of freedom (Nphys = 5). The framework develops the closed-time-path (CTP) open-quantum-system description, stochastic torsional backreaction, and renormalized nonlocal effective actions. Furthermore, the analysis extends to homogeneous anisotropic (Bianchi type I) and isotropic FLRW cosmological backgrounds, deriving linear perturbation equations, helicity-resolved tensor propagation, and parity-odd torsional response (gravitational birefringence) without relying on ad-hoc phenomenological parameters.