Non-extensivity Effects and the Highest Energy Cosmic Ray Affair
  Recent measurements of the cosmic microwave background confirm that it is described by a Planckian distribution with high precision. It is non-extensivity bounded to be less than some parts in $10^5$, or to some parts in $10^4$ at most. This deviation may appear minuscule, but may have a non-negligible effect on a particle propagating through this background over the course of millions of years. In this paper we analyze the possible influence of such a slight deviation upon the propagation of nuclei and protons of ultra-high energy. These particles interact via photopion and photodisintegration processes which we examine taking into account a slight non-extensive background. We show that such a deviation does not exhibit a significant difference in the energy attenuation length of extremely high energy cosmic rays. 
Luis A. Anchordoqui and Diego F. Torres