  We consider the general expressions for the time delay of photons of
different energies in the framework of multi-dimensional cosmological models.
In models with compactified extra-dimensions (Kaluza-Klein type models), the
main source of the photon time delay is the time variation of the
electromagnetic coupling, due to dimensional reduction, which induces an
energy-dependence of the speed of light. A similar relation between the fine
structure constant and the multi-dimensional gauge couplings also appears in
models with large (non-compactified) extra-dimensions. For photons of energies
around 1 TeV, propagating on cosmological distances in an expanding Universe,
the time delay could range from a few seconds in the case of Kaluza-Klein
models to a few days for models with large extra-dimensions. As a consequence
of the multi-dimensional effects, the intrinsic time profiles at the emitter
rest frame differ from the detected time profiles. The formalism developed in
the present paper allows the transformation of the predicted light curves of
various energy ranges of the emitter into the frame of the observer, for
comparison with observations. Therefore the study of energy and redshift
dependence of the time delay of photons, emitted by astrophysical sources at
cosmological distances, could discriminate between the different
multi-dimensional models and/or quantum gravity effects.
