Acausality in Superfluid Dark Matter and MOND-like Theories
  There has been much interest in novel models of dark matter that exhibit
interesting behavior on galactic scales. A primary motivation is the observed
Baryonic Tully-Fisher Relation in which the mass of galaxies increases as the
quartic power of rotation speed. This scaling is not obviously accounted for by
standard cold dark matter. This has prompted the development of dark matter
models that exhibit some form of so-called MONDian phenomenology to account for
this galactic scaling, while also recovering the success of cold dark matter on
large scales. A beautiful example of this are the so-called superfluid dark
matter models, in which a complex bosonic field undergoes spontaneous symmetry
breaking on galactic scales, entering a superfluid phase with a 3/2 kinetic
scaling in the low energy effective theory, that mediates a long-ranged MONDian
force. In this work we examine the causality and locality properties of these
and other related models. We show that the Lorentz invariant completions of the
superfluid models exhibit high energy perturbations that violate global
hyperbolicity of the equations of motion in the MOND regime and can be
superluminal in other parts of phase space. We also examine a range of
alternate models, finding that they also exhibit forms of non-locality.
