  Ultra-high energy cosmic rays interacting with the radiation fields in the
universe cause electromagnetic cascades resulting in a flux of extragalactic
gamma rays, detectable to some 100 GeV. Recent precise measurements of the
extragalactic gamma ray flux by Fermi-LAT, coupled with estimates of the
background from active galactic nuclei of various types, allows limits to be
set on the cascade component. By comparison with prediction and, making various
assumptions, ie taking a particular model, limits can be set on the maximum
energy to which ultra-high energy particle can be accelerated.
  If our model is correct, it is unlikely that the maximum energy is above 100
EeV, in turn, the apparent 'GZK' cut-off in the measured ultra-high energy
spectrum could instead be due to a fall-off in the intrinsic emergent particle
spectrum. However, it is not plausible to be dogmatic at the present time
because of uncertainty in many of the parameters involved. We have used recent
estimates of the range of parameters and have found that although our model has
parameters in the allowable ranges the uncertainties are so large that our
result is not unique, although the method is satisfactory. The result must
thus, so far, be taken as an indication only.
