Gravity-mediated modifications of the dispersion relation in nontrivial backgrounds

Radiative corrections evaluated in nontrivial backgrounds lead to dispersion relations which effectively break the local Lorentz symmetry even if Lorentz invariance holds at a fundamental level. We report on progress made toward the calculation of radiative corrections which are induced by gravity. These should be relevant when approaching Planck scale. We first present the properties of the self-energy of a scalar particle traveling in a thermal graviton bath. We then discuss the possibility of performing the corresponding calculation in a curved background. We give the connection between two different approaches to the dispersion relation, based on the self-energy and the effective action, and we emphasize the need for the closed-time-path formalism in curved backgrounds.