Dissipative Quantum Gravity: Foundations, Stability, and Emergent Spacetime Architecture

Abstract

Contraction of the complex Quantum Geometric Tensor across an 8D bipartite Hilbert space $\mathcal{H}_8 = \mathcal{H}_\text{NH} \otimes \mathcal{H}_\text{Herm}$ constructs a four-dimensional manifold with dynamic $(-,+,+,+)$ Lorentzian metric signature. Near the second-order Exceptional Point boundary $u \to 1^+$, physical coordinate time scales logarithmically, shifting the initial cosmological boundary to past infinity ($t \to -\infty$) and guaranteeing geodesic completeness ($s \to -\infty$) while maintaining a bounded Kretschmann curvature scalar $K = 12/\ell_P^4$. Temporal kinetic matrix evaluation for scalar doublet perturbations establishes the strict stability condition $Q \equiv 1 - \gamma^2 > 0$, which prevents Ostrogradsky ghost instabilities for multi-field couplings $|\gamma| < 1$. Open-system Functional Renormalization Group flow integrates out ultraviolet modes down to the infrared horizon scale $k_\text{IR} = H_0 \sim 10^{-60} M_P$, screening the bare Planckian vacuum energy to the observed cosmological constant $\Lambda(H_0) \sim 10^{-120} M_P^2$. Open-system relaxation generates a dissipative effective pressure $p_{\text{eff}} = p - \tilde{\gamma}\rho$ that naturally violates the Strong Energy Condition without requiring ad hoc inflaton potentials or fundamental dark energy fields.