ABSTRACT
Recently there have been exciting developments in astrophysics and cosmology, associated with observations of ultra high energy cosmic rays (UHECR), of energies larger than 1020 eV [1], as well as high-redshift (z ~ 1) supernovae observations [2] claiming a current-era acceleration of the Universe. The latter observations, when combined with data from measurements of the cosmic microwave background radiation [3], which provide evidence for a spatially flat universe, with a Qtotai = 1, seem to indicate that up to 70 % of the total energy density of the Universe is attributed to a dark energy component, which could be a positive cosmological constant (de Sitter type Universe) Λ or something else. On the other hand, the presence of UHECR events appears puzzling from the point of view of Lorentz Invariance [4, 5, 6]. The latter symmetry would impose an energy threshold (Greitsen-Zatsepin-Kuzmin (GZK) cut off) [7] above which certain reactions can occur which would prevent such UHECR events to reach the observation point, if one makes the physically plausible assumption tha t such events come from extragalactic sources [1].
