Ultra-large distance modification of gravity from Lorentz symmetry breaking at the Planck scale

We present an extension of the Randall–Sundrum model in which, due to spontaneous Lorentz symmetry breaking, graviton mixes with bulk vector fields and becomes quasilocalized. The masses of KK modes comprising the four-dimensional graviton are naturally exponentially small. This allows to push the Lorentz breaking scale to as high as a few tenth of the Planck mass. The model does not contain ghosts or tachyons and does not exhibit the van Dam–Veltman–Zakharov discontinuity. The gravitational attraction between static point masses becomes gradually weaker with increasing of separation and gets replaced by repulsion (antigravity) at exponentially large distances.