Constraints on extra-dimensions and variable constants from cosmological   gamma ray bursts
  The observation of the time delay between the soft emission and the high-energy radiation from cosmological gamma ray bursts can be used as an important observational test of multi-dimensional physical theories. The main source of the time delay is the variation of the electromagnetic coupling, due to dimensional reduction, which induces an energy dependence of the speed of light. For photons with energies around 1 TeV, 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. Based on these results we suggest that the detection of the 18-GeV photon $ \sim $4500 s after the keV/MeV burst in GRB 940217 provides a strong evidence for the existence of extra-dimensions. The time delay of photons, if observed by the next generation of high energy detectors, like, for example, the SWIFT and GLAST satellite based detectors, or the VERITAS ground-based TeV gamma-ray instrument, could differentiate between the different models with extra-dimensions. 
T. Harko, K. S. Cheng