Particle propagation and effective space-time in gravity’s rainbow

Based on the results obtained in our previous study on gravity’s rainbow, we determine the quantum corrections to the space-time metric for the Schwarzschild and the de Sitter background, respectively. We analyze how quantum fluctuations alter these metrics, inducing modifications on the propagation of test particles. Significantly enough, we find that quantum corrections can become relevant not only for particles approaching the Planck energy but, due to the one-loop contribution, even for low-energy particles as far as Planckian length scales are considered. We briefly compare our results with others obtained in similar studies and with the recent experimental OPERA announcement of superluminal neutrino propagation.