Completing Lorentz violating massive gravity at high energies
  Theories with massive gravitons are interesting for a variety of physical
applications, ranging from cosmological phenomena to holographic modeling of
condensed matter systems. To date, they have been formulated as effective field
theories with a cutoff proportional to a positive power of the graviton mass
m_g and much smaller than that of the massless theory (M_P ~ 10^19 GeV in the
case of general relativity). In this paper we present an ultraviolet completion
for massive gravity valid up to a high energy scale independent of the graviton
mass. The construction is based on the existence of a preferred time foliation
combined with spontaneous condensation of vector fields. The perturbations of
these fields are massive and below their mass the theory reduces to a model of
Lorentz violating massive gravity. The latter theory possesses instantaneous
modes whose consistent quantization we discuss in detail. We briefly study some
modifications to gravitational phenomenology at low-energies. The homogeneous
cosmological solutions are the same as in the standard cosmology. The
gravitational potential of point sources agrees with the Newtonian one at
distances small with respect to m_g^(-1). Interestingly, it becomes repulsive
at larger distances.
