  In a recent paper (arXiv:1412.6000) a general mechanism for emergence of
cosmological space-time geometry from a quantum gravity setting was devised and
departure from standard dispersion relations for elementary particle were
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 scenarios
showing that space-time will have to be by nowadays classical to a very high
degree in order to be consistent with current observations.
