  We investigate the production of cosmic ray (CR) protons at cosmological
shocks by performing, for the first time, numerical simulations of large scale
structure formation that include directly the acceleration, transport and
energy losses of the high energy particles. CRs are injected at shocks
according to the thermal leakage model and, thereafter, accelerated to a
power-law distribution as indicated by the test particle limit of the diffusive
shock acceleration theory. The evolution of the CR protons accounts for losses
due to adiabatic expansion/compression, Coulomb collisions and inelastic p-p
scattering. Our results suggest that CR protons produced at shocks formed in
association with the process of large scale structure formation could amount to
a substantial fraction of the total pressure in the intra-cluster medium. Their
presence should be easily revealed by GLAST through detection of gamma-ray flux
from the decay of neutral pions produced in inelastic p-p collisions of such CR
protons with nuclei of the intra-cluster gas. This measurement will allow a
direct determination of the CR pressure contribution in the intra-cluster
medium. We also find that the spatial distribution of CR is typically more
irregular than that of the thermal gas because it is more influenced by the
underlying distribution of shocks. This feature is reflected in the appearance
of our gamma-ray synthetic images. Finally, the average CR pressure
distribution appears statistically slightly more extended than the thermal
pressure.
