The assumption of Lorentz invariance is one of the founding principles of Modern Physics and violation of it would have profound implications to our understanding of the universe. For instance, certain theories attempting a unified theory of quantum gravity predict there could be an effective refractive index of the vacuum; the introduction of an energy dependent dispersion to photons could in turn lead to an observable Lorentz invariance violation signature. Whilst a very small effect on local scales the effect will be cumulative, and so for very high energy particles that travel very large distances the difference in arrival times could become sufficiently large to be detectable. This proceedings will look at testing for such Lorentz invariance violation (LIV) signatures in the astronomical lightcurves of gamma-ray emitting objects, with particular notice being given to the prospects for LIV testing with, the next generation observatory, the Cherenkov Telescope Array.

3 pages. To be published in the proceedings of NOW2014