Time delay of photons of different energies in multidimensional cosmological models

Abstract

We consider the general expressions for the time delay of photons of different energies in the framework of multidimensional 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 multidimensional gauge couplings also appears in models with large (non-compactified) extra dimensions. For photons of energies around 1 TeV propagating at 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 multidimensional 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 the energy and redshift dependence of the time delay of photons emitted by astrophysical sources at cosmological distances could discriminate between the different multidimensional models and/or quantum gravity effects.