The Cosmological Constant and MOND Acceleration Scale as Emergent Features of a Stochastic Graviton Bunch-Davies Vacuum

This paper presents a phenomenological framework that geometrically connects the Modified Newtonian Dynamics (MOND) acceleration scale with the cosmological Hubble horizon. By investigating the stochastic gravitational background, we derive a geometric factor of 4/3 originating from the spin-2 tensor polarization average. When this geometric correction is applied, the local MOND acceleration scale (a₀) naturally aligns with the global expansion rate of the universe. Crucially, this alignment provides a direct, parameter-free resolution to the H₀ tension, bridging the gap between early-universe and late-universe measurements. Furthermore, the model provides sharp, falsifiable predictions regarding galactic dynamics. We demonstrate that the External Field Effect (EFE) is highly sensitive to the local cosmic environment. The framework predicts a systematic 16% offset in the Baryonic Tully-Fisher Relation (BTFR) between galaxies residing in deep cosmic voids compared to those located within dense galaxy clusters. This offset offers a clear, testable signature using current integral-field spectroscopy datasets.