  In the past decade the phenomenology of quantum gravity has been dominated by
the search of violations of Lorentz invariance. However, there are very serious
arguments that led us to assume that this invariance is a symmetry in Nature.
This motivated us to construct a phenomenological model describing how a
Lorentz invariant granular structure of spacetime could become manifest. The
proposal is fully covariant, it involves non-trivial couplings of curvature to
matter fields and leads to a well defined phenomenology.
