  It is shown that a quadratic gravitational Lagrangian in the Palatini
formulation is able to capture different aspects of quantum gravity
phenomenology in a single framework. In particular, in this theory field
excitations propagating with different energy-densities perceive different
background metrics, a fundamental characteristic of the DSR and Rainbow Gravity
approaches. This theory, however, avoids the so-called soccer ball problem.
Also, the resulting isotropic and anisotropic cosmologies are free from the big
bang singularity. This singularity avoidance occurs non-perturbatively and
shares some similitudes with the effective dynamics of loop quantum cosmology.
