  We have calculated the dispersion relation for the high energy cosmic rays
(protons, electrons and neutrinos) propagating in the Bose gas as well as Bose
condensate medium of the pseudo-scalar particles. For cosmic rays propagating
in the Bose gas, the mass of the particle will decrease and this is
proportional to the boson density in the medium. If the propagating fermion is
massless then it will develop an imaginary mass and thus will be absorbed in
the medium. But if the condition $m^2/m_{\phi}p_0\simeq 1$ is satisfied, then
the cosmic rays will propagate freely without loosing energy in the Bose
condensate medium.
