Massive gravity with anisotropic scaling

We study a massive gravity theory which is Lorentz-violating all the way from ultraviolet to infrared energy scales. At short distances the theory breaks diffeomorphism invariance and time and space scale differently. Dynamical metric fields are introduced which, upon linearization over a Minkowski background, correspond to Lorentz-violating mass terms at large distances. We perform a scalar perturbation analysis and we show that with an appropriate choice of parameters, the theory is healthy without ghosts, tachyons, strong coupling problems, and instabilities.