Induced Quantum Gravity from Vacuum EntanglementField Equations PPN Analysis and the Cosmological Constant

We construct the field equations of the TTE-EPR framework, in which the spacetime metric is not afundamental field but the Fisher–Bures pullback of the vacuum entanglement map λ : M4 → M, whereM = Sp(56,R)/U(28) is the Siegel upper half-space parametrizing the squeezed vacuum of the StandardModel. The action is a nonlinear σ-model of Born–Infeld type, with the vacuum entanglement parametersλa(x) as the sole dynamical variables. We derive the Euler–Lagrange field equations, demonstrate thatEinstein’s equations emerge in the adiabatic limit via the Sakharov induced gravity mechanism, and performthe complete Parametrized Post-Newtonian (PPN) analysis: all ten PPN parameters take their generalrelativisticvalues (γ = β = 1, all others zero) with corrections of order (lPl/rs)2 ∼ 10−76 for the Sun.The cosmological constant is reinterpreted as the scalar curvature of (M, gFB)—a dynamical field ΛFB(x)determined by the purity of the local vacuum state, bounded below and positive, dissolving the 122-orderof-magnitude discrepancy by removing the double-counting of vacuum energy. We analyze the strong-fieldregime near black hole horizons, where the finite vacuum processing rate ˜ηmax ∼ 5×1042 provides a naturaltrans-Planckian cutoff resolving the Hawking spectrum UV problem. Internal modes of M that do notproject onto gμν produce ∇˜η ̸= 0 in regions of flat spacetime, providing a dark-matter phenomenologywithout additional particles. Stress tests in ten extreme regimes confirm internal consistency. All resultsfollow from Paper I 1 with no additional free parameters.