Cosmic Rays Propagation in Bose Condensed Dark Matter

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.