Speaker
Description
Lorentz Invariance (LI) states that the structure of space-time is identical for all observers. However, several quantum gravity models suggest that this symmetry could be violated when approaching the Planck scale. Even a small violation of LI could significantly affect the propagation of Ultra-High-Energy Cosmic Rays (UHECRs) over cosmological distances. Moreover, at the extreme energies reached in UHECR interactions with the atmosphere, modifications in the development of Extensive Air Showers (EAS) are expected. In this contribution, the possible effects of Lorentz Invariance Violation (LIV) are discussed within a phenomenological framework, where LIV is introduced as a perturbative term in the single-particle dispersion relation. Such a modification alters the kinematics of particle interactions both during the extragalactic propagation of cosmic rays and during the development of the atmospheric shower. Recent studies on LIV are presented and discussed in connection with the measurements performed by the Pierre Auger Observatory. The impact of different LIV scenarios is investigated through the comparison with the observed energy spectrum, the inferred mass composition, and the upper limits on the photon flux. Particular attention is devoted to the development of the air-shower cascade in the atmosphere. At the energies involved in UHECR interactions, LIV effects could significantly modify particle production and decay channels, potentially leading to observable deviations in the shower evolution. In this context, the distribution of the muon content in extensive air showers represents a particularly sensitive observable, providing a powerful probe to test and constrain LIV scenarios.