The mainstream MOND hypothesis purports different behaviour below some acceleration threshold. Is there some other theory in which gravity would behave differently based on some other condition? I wonder if outer regions of galaxies could rotate faster than expected due to some kind of galactic frame-dragging of the inner regions. Mach's principle has a related idea: "mass out there influences inertia here".
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You can reformulate MOND's acceleration in terms of cosmological parameters as $a_0 = c^2 / R_u$ with $R_u$ the radius of the observable universe. For instance, quantized inertia theories rely on this relationship.