  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 cut-off. 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.
