Modified gravity approach based on a preferred time foliation
  We propose, in a heuristic way, a relativistic modified gravity model as an
alternative to particle dark matter at galactic scales. The model is based on a
postulated preferred time foliation described by a dynamical scalar field
called the "Khronon". In coordinates adapted to the foliation it appears as a
modification of general relativity violating local Lorentz invariance in a
regime of weak gravitational fields. The model is a particular case of
non-canonical Einstein-aether theory, but in which the aether vector field is
hypersurface orthogonal. We show that this model recovers the phenomenology of
the modified Newtonian dynamics (MOND) in the non-relativistic limit, and
predicts the same gravitational lensing as general relativity but with a
modified Poisson-type potential.
