Studies on deviations from Lorentz invariance

Lorentz invariance is a cornerstone of quantum field theories and general relativity. To date, no violation of such a symmetry has been experimentally detected. Nevertheless, certain quantum gravity theories possess mechanisms that can lead to deviations from Lorentz invariance, particularly effects arising from modifications of space-time are expected to appear at distances of the order of the Planck length. In this talk, I will discuss the motivations and studies of some Lorentz-violating models. Results on gravitational quantum states of ultracold neutrons affected by Lorentz- and CPT-violating terms are presented. Finally, I will discuss about the viability to introduce spontaneous Lorentz symmetry breaking by means of the Plebanski model, which is a first order theory of nonlinear electrodynamics.