  Observations in radio have shown that galaxy clusters are giant reservoirs of
cosmic rays (CR). Although a gamma- ray signal from the cluster volume is
expected to arise through interactions of CR protons with the ambient plasma, a
confirming observation is still missing. We search for a cumulative gamma-ray
emission in direction of galaxy clusters by analysing a collection of stacked
Fermi-LAT count maps. Additionally, we investigate possible systematic
differences in the emission between cool-core and non-cool core cluster
populations. Making use of a sample of 53 clusters selected from the HIFLUGCS
catalog, we do not detect a significant signal from the stacked sample. The
upper limit on the average flux per cluster derived for the total stacked
sample is at the level of a few 1e-11 ph cm-2 s-1 at 95% confidence level in
the 1-300 GeV band, assuming power-law spectra with photon indices 2.0, 2.4,
2.8 and 3.2. Separate stacking of the cool core and non-cool core clusters in
the sample lead to similar values of around 5e-11 ph cm-2 s-1 and 2e-11 ph cm-2
s-1, respectively. Under the assumption that decaying pi0, produced in
collisions between CRs and the ambient thermal gas, are responsible for the
gamma-ray emission, we set upper limits on the average CR content in galaxy
clusters. For the entire cluster population, our upper limit on the gamma-ray
flux translates into an upper limit on the average CR-to-thermal energy ratio
of 4.6% for a photon index of 2.4, although it is possible for individual
systems to exceed this limit. Our 95% upper limits are at the level expected
from numerical simulations, which likely suggests that the injection of CR at
cosmological shocks is less efficient than previously assumed.
