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 mg and much smaller than that of the massless theory (MP ≈ 1019 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 mg−1. Interestingly, it becomes repulsive at larger distances.