Post-Newtonian constraints on Lorentz-violating gravity theories with a
  MOND phenomenology
  We study the post-Newtonian expansion of a class of Lorentz-violating gravity
theories that reduce to khronometric theory (i.e. the infrared limit of Horava
gravity) in high-acceleration regimes, and reproduce the phenomenology of the
modified Newtonian dynamics (MOND) in the low-acceleration, non-relativistic
limit. Like in khronometric theory, Lorentz symmetry is violated in these
theories by introducing a dynamical scalar field (the "khronon") whose gradient
is enforced to be timelike. As a result, hypersurfaces of constant khronon
define a preferred foliation of the spacetime, and the khronon can be thought
of as a physical absolute time. The MOND phenomenology arises as a result of
the presence, in the action, of terms depending on the acceleration of the
congruence orthogonal to the preferred foliation. We find that if the theory is
forced to reduce exactly to General Relativity (rather than to khronometric
theory) in the high-acceleration regime, the post-Newtonian expansion breaks
down at low accelerations, and the theory becomes strongly coupled.
Nevertheless, we identify a sizeable region of the parameter space where the
post-Newtonian expansion remains perturbative for all accelerations, and the
theory passes both solar-system and pulsar gravity tests, besides producing a
MOND phenomenology for the rotation curves of galaxies. We illustrate this
explicitly with a toy model of a system containing only baryonic matter but no
Dark Matter.
