Plausible Sources of Dark Energy and Associated Vacuum Properties: Implications for Newton’s G, MOND’s a0, Vacuum Invariants, and the Tully–Fisher and Faber–Jackson Galactic Relations

We believe that the origin of the universal dark energy may crucially depend on the behavior of the gravitational constant G. If G is constant throughout the universe, then the dark energy density u0 is supported by the vacuum via its constant and evolving properties. On the other hand, in varying-G gravity (whose low-acceleration limit is MOND), u0 is a manifestation of radial G-gradients in the source of gravity. We estimate the present-day dark energy density of the universe in these two independent cases without using conventional Planck-2018 modeling in deriving the expressions for u0. The constant-G derivation uses dimensional analysis, vacuum constants, and a newly discovered evolving bridge between vacuum mechanical and electromagnetic quantities. The varying-G derivation relies on the MOND critical acceleration a0, the source of gravity that falls off as ∼r−2 at large distances r, and the assumption that the present-day energy density u0 can be estimated by spatially averaging this radial profile over the MOND volume 4π3r03, where r0=c2/a0 and c is the speed of light in vacuum. The agreement between these two determinations and the Planck-2018 results from ΛCDM modeling is at the percent level, so that the results cannot distinguish clearly between constant-G and varying-G gravity. The analysis further indicates that the Newtonian constant G0, the MOND constant a0, and the Planck units of force, power, voltage, and current can be regarded as empirical vacuum constants within the proposed framework, alongside the well-known resistive properties of the vacuum, whereas charge, capacitance, inductance, and various fields are scale-dependent properties evolving in the expanding universe since the Stoney era. Ultimately, the vacuum behaves as a remarkably stiff elastic medium under stress, irrespective of the presence or absence of matter. This property has long been encoded, albeit inconspicuously, in the much discussed Tully–Fisher and Faber–Jackson relations, as well as in the Casimir effect and the field equations of General Relativity.