Dynamical Vacuum Stabilization from Holographic Entanglement: A Scalar-Tensor Framework to Address the Hubble Tension and Cosmological Accelerations

Abstract: This research presents the MTM-VG 6.0 framework, a robust scalar-tensor model that provides a unified dynamical resolution to the vacuum energy hierarchy problem and the Hubble tension. Unlike static cosmological constant models, this framework derives dark energy as a dynamical consequence of holographic information saturation. Key Scientific Contributions: - Holographic Origin: The effective potential V(Phi) is derived from the first law of entanglement entropy using the Ryu-Takayanagi formula. - Mathematical Stability: Global stability is proven using a Lyapunov functional analysis, identifying dark energy as a global attractor. - Hubble Tension Resolution: The model predicts a dynamical shift in the local expansion rate (approx. 5-7%), reconciling SH0ES measurements with Planck CMB data. - Observational Predictions: The framework provides specific signatures for the effective gravitational coupling (Geff) and structure growth rate (f sigma 8). Author: Mohammad Abdel-Haseeb Mesbah ORCID: 0009-0007-9973-9671 Version: 6.0