  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.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory