Doubly Special Relativity with a minimum speed and the search for a   quantum gravity at low energies
  This research aims to consider a new principle of symmetry in the space-time by means of the elimination of the classical idea of rest including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by the particles, represents a preferred inertial reference frame associated with a cosmological background field that breaks Lorentz symmetry. So there emerges a modified relativistic dynamics with a minimum speed related to the Planck length of the early universe, which leads us to search for a quantum gravity at low energies. 
Cl\'audio Nassif
gr-qc