A Proposal for Testing Gravity's Rainbow

Various approaches to quantum gravity such as string theory, loop quantum gravity and Horava-Lifshitz gravity predict modifications of the energy-momentum dispersion relation. Magueijo and Smolin incorporated the modified dispersion relation (MDR) with the general theory of relativity to yield a theory of gravity's rainbow. In this paper, we investigate the Schwarzschild metric in the context of gravity's rainbow. We investigate rainbow functions from three known modified dispersion relations that were introduced by Amelino-Camelia, et el. in [arXiv:hep-th/9605211, arXiv:0806.0339v2, arXiv:astro-ph/9712103] and by Magueijo-Smolin in [arXiv:hep-th/0112090]. We study the effect of the rainbow functions on the deflection of light, photon time delay, gravitational red-shift, and the weak equivalence principle. We compare our results with experiments to obtain upper bounds on the parameters of the rainbow functions.