Mem-Force Theory: A Unified Framework of Vacuum Restoring Force Across QCD, Galaxies, Black Holes and Cosmology

Based on the physical picture of vacuum as a responsive medium and matter as perturbations, we construct a modified theory of gravity centered on density-dependent vacuum restoring force, known as Mem-Force Theory. This theory interprets gravity as the restoring response of the vacuum to matter perturbations, introducing a scalar mem-force field and a density-dependent restoring parameter that follows a power-law scaling relation: μ (ρ) = μ₀ (ρ/ρ₀) ^α. Using rotation curve data of 15 galaxies from the SPARC database, we obtain the universal exponent α = 0. 385 ± 0. 02. This value is consistent with the first-principles result from QCD sum rules, α = 3/8 = 0. 375, within the 1σ error range. With the chameleon screening mechanism, the theory is compatible with high-precision solar-system tests. It provides a unified description of galactic dynamics, strong-field gravity, cosmic evolution, and nonperturbative QCD effects. Testable predictions include black hole shadow shift (~0. 5%), gravitational-wave scalar polarization (AS/AT ~ 10⁻⁶), gravitational-wave dispersion (Δv/c ~ 10⁻¹⁵), dark-energy equation of state (w₀ = -0. 98 ± 0. 01), and laboratory fifth-force (αₑff ~ 5×10⁻⁸). These predictions can be tested by SKA, EHT, LIGO, LISA, Euclid, and table-top precision experiments. This paper presents a falsifiable, self-consistent, unified framework whose validity will be determined by multi-messenger observations in the next 5-20 years.