More about spontaneous Lorentz-violation and infrared modification of gravity

We consider a model with Lorentz-violating vector field condensates, in which dispersion laws of all perturbations, including tensor modes, undergo non-trivial modification in the infrared. The model is free of ghosts and tachyons at high 3-momenta. At low 3-momenta there are ghosts, and at even lower 3-momenta there exist tachyons. Still, with appropriate choice of parameters, the model is phenomenologically acceptable. Beyond a certain large distance scale and even larger time scale, the gravity of a static source changes from that of General Relativity to that of van Dam-Veltman-Zakharov limit of the Fierz-Pauli theory. Yet the late time cosmological evolution is always determined by the standard Friedmann equation, modulo small correction to the "cosmological Planck mass", so the modification of gravity cannot by itself explain the accelerated expansion of the Universe. The latter property is generic in a wide class of models with condensates.