LORENTZ INVARIANCE VIOLATION EFFECTS ON ULTRA HIGH ENERGY COSMIC RAYS PROPAGATION: A GEOMETRICAL APPROACH

Cosmic rays are highly energetic extraterrestrial particles, mainly originated outside the Solar system, with energy that spans many decades. Since they include the most energetic particles, accessible nowadays, it is very interesting to study this kind of radiation, that constitute a significant source of informations about astrophysical objects. Moreover these highly energetic particles propagate for cosmological distances, so they can furnish a deeper understanding of the physical mechanisms of the universe. Hence it results very important to obtain a deeper understanding of the so called GZK “puzzle”. Universe results opaque to the propagation of the highest energetic particles, because of their interaction with the Cosmic Microwave Background Radiation (CMBR). Therefore the sources of these Ultra High Energy Cosmic Rays (UHECR) must be collocated inside a foreseen opacity sphere (GZK effect). But some recent experimental observations seem to indicate the possibility that certain UHECR correlate with candidate sources collocated farther than expected. One of the most interesting possible explanations of this GZK suppression “puzzle” consists in introducing a particle kinematics modification, assuming this effect as a relic of the supposed quantum structure of space-time. In this respect, physics is amended by the introduction of small perturbations to the Lorentz symmetry, the so called Lorentz Invariance Violation (LIV) scenario. In this work, to preserve the idea of space-time homogeneity and isotropy, a possible way to introduce a LIV theory, without a preferred class of inertial observers, is explored. The Lorentz symmetry is therefore only modified, as in Doubly Special Relativity theories. Thus the idea of space-time isotropy results restored respect to the new amended Lorentz transformations, here introduced. Hence it results possible to solve the GZK “puzzle” without the necessity of the introduction of a privileged class of inertial observers. The geometry of space-time is constructed starting from the momentum space modified structure, determined by the amended particle kinematics. The resultant geometry is of Finsler type, with an acquired energy dependance. The Lorentz group is then modified, in order to preserve space-time isotropy. The particle Standard Model results modified, but it still preserve the symmetry structure of the ordinary one, as shown proving the validity of the Coleman-Mandula theorem, with the substitution of the ordinary Lorentz group with the modified one. Finally the model is employed to compute phenomenological predictions on the behavior of UHECR and even of high energy neutrinos.