  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.
