ar X iv : a st ro - p h / 03 04 10 0 v 1 5 A pr 2 00 3 Ultra - High Energy Cosmic Rays and Absolute Reference Frame defined by External Field

High-energy end of the cosmic-ray spectrum has provided us to check a validity of the Lorentz Invariance and the Relativity principle, through the observation of the so-called GZK cutoff. It is claimed in this report that the comoving reference frame in the expanding universe might define the preferable inertia frame, in contradiction to the relativity principle. If the present universe has been permeated by tensor fields in a manner like it has been done by Higgs scalar field , the limiting particle velocity of each species splits to different values depending on the coupling coefficients to these external fields. Energy spectrum of the cosmic rays extends by a power-law over more than ten decimal, decreasing in a power-law like E −γ with energy E and γ ∼ 2.5. Then a natural question is whether the high-energy end in the energy spectrum does exist or not. In 1966, a very clear-cut prediction was presented, which introduced a definite upper-limit in the power-low energy spectrum, which is called now as GZK(Greisen-Zatepin-Kuzmin) cutoff .[1] This cutoff prediction was invoked by the discovery of " 3K radiation " in 1965, which is now called as CMB(cosmic microwave background). Although CMB was observed just on the earth, CMB was supposed to fill up in the whole cosmic space uniformly, even in the extra-galactic space, as the relics of " hot " big-bang. Therefore it became crucial to check the presence of CMB in the extra-galactic space, in order to settle the big debates between the steady state cosmology and Gamow's hot big-bang cosmology. As an advocator of the steady-state cosmology, Fred Hoyle tried hard to present two types of counter arguments, one was about exotic interstellar dusts which masks the extragalactic view in this wave-band and another one was how much degree the high-energy 1