The Rise and The Fall of Quantum Vacuum How Dark Matter Rewrites the Laws of Gravity 2.0

The first version of the manuscript primarily presented a conceptual framework, emphasizing physical intuition and phenomenological motivation while leaving several structural elements implicit.In the revised version, the theory is reformulated within a fully covariant action-based framework, providing explicit dynamical equations and closure relations.The tensor field Ψμν\Psi_{\mu\nu}Ψμν is no longer ambiguously described as an induced metric perturbation, but is clearly defined as an independent dynamical degree of freedom.Interaction terms are now derived from the action, ensuring consistency with conservation laws and the Bianchi identities.The coupling parameter β\betaβ, previously discussed qualitatively, is now specified as an explicit density-dependent function, enabling numerical implementation.Temporal nonlocality and gravitational hysteresis are formalized through a causal memory kernel and an equivalent differential formulation.Stability and degree-of-freedom control are explicitly addressed within an effective field theory perspective.The relation between the response field and standard gravitational waves is clarified, avoiding conflation with the graviton.Overall, the revised version transforms the model from a heuristic proposal into a mathematically well-defined and testable theoretical framework.