Additional energy gain of charged particle moving in CMB

Abstract

The problem of ultra high energy charged particles motion in the cosmic microwave background (CMB) is considered. It is shown that the exact solutions of the relativistic equation for charged particle motion in plane electromagnetic waves, when initial conditions are imposed on coordinate and time of the wave results in an additional energy gain of particle after averaging over initial random phases of the waves. Thus, there is no Greisen-Zatsepin-Kuzmin (GZK) cut-off during propagation of ultra high energy charged particles within the CMB. This situation is similar to the infrared situation in Quantum Electrodynamics: despite the presence of many low-energy photons and multiquantum exchange of energy with the charged particle, the main process - here is the propagation of charged particle of UHECR within the CMB, remains almost unchanged, if we are not interested in delicate distinctions of the process, such as small angle deviations of trajectory from the rectilinear line.