A critique of covariant emergent gravity

I address some problems encountered in the formulation of relativistic models encompassing the MOND phenomenology of radial acceleration. I explore scalar and vector theories with fractional kinetic terms and f(R)-type gravity, demanding that the energy density be bounded from below and that superluminal modes be absent, but also that some consistency constraints with observational results hold. I identify configurations whose energy is unbounded from below and formulate some no-go statements for vector field models and modified gravity theories. Finally, I discuss superfluid dark matter as a hybrid theory lying between cold dark matter and modified gravity, highlighting some difficulties present also in this case, which appears preferable to the others.