Modified MOND Inertia and Covariant Vacuum State

In this paper, we investigate the inertia of macroscopic objects using a mean field approach. The dynamics are given by the equation of the Kuramoto-like form. The equilibrium solution of the equation is consistent with MOND theory. As a result, the state of the universe at large scales enters local dynamics in small systems. We also show that the vacuum energy density arising from zero-point fluctuations and symmetry breakings is acceleration-dependent. By requiring that the vacuum state is covariant, all acceleration-dependent vacuum energy should be regarded as non-physical.