Phenomenology of effective geometries from quantum gravity

In a recent paper [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015)] a general mechanism for the emergence of cosmological spacetime geometry from a quantum gravity setting was devised and a departure from standard dispersion relations for an elementary particle was predicted. We elaborate here on this approach extending the results obtained in that paper and showing that generically such a framework will not lead to higher order modified dispersion relations in the matter sector. Furthermore, we shall discuss possible phenomenological constraints to this scenario showing that spacetime will have to be classical to a very high degree by now in order to be consistent with current observations.