Structure formation in the intergalactic medium ( IGM ) produces large-scale , collisionless shock waves , where electrons can be accelerated to highly relativistic energies .
Such electrons can Compton scatter cosmic microwave background photons up to \gamma -ray energies .
We study the radiation emitted in this process using a hydrodynamic cosmological simulation of a \Lambda \mbox { CDM } universe .
The resulting radiation , extending beyond TeV energies , has roughly constant energy flux per decade in photon energy , in agreement with the predictions of Loeb & Waxman ( 2000 ) .
Assuming that a fraction \xi _ { e } = 0.05 of the shock thermal energy is transferred to the population of accelerated relativistic electrons , as inferred from collisionless non-relativistic shocks in the interstellar medium , we find that the energy flux of this radiation , \epsilon ^ { 2 } ( dJ / d \epsilon ) \simeq 50 - 160 \mbox { eV cm } ^ { -2 } \mbox { s } ^ { -1 } \mbox { sr } ^ { -1 } , constitutes \sim 10 \% of the extragalactic \gamma -ray background flux .
The associated \gamma -ray point-sources are too faint to account for the \sim 60 unidentified EGRET \gamma -ray sources , but GLAST should detect and resolve several \gamma -ray sources associated with large-scale IGM structures for \xi _ { e } \simeq 0.03 , and many more sources for larger \xi _ { e } .
The intergalactic origin of the shock-induced radiation can be verified through a cross-correlation with , e.g. , the galaxy distribution that traces the same structure .
Its shock-origin may be tested by cross-correlating its properties with radio synchrotron radiation , emitted as the same accelerated electrons gyrate in post-shock magnetic fields .
We predict that GLAST and Čherenkov telescopes such as MAGIC , VERITAS and HESS should resolve \gamma -rays from nearby ( redshifts z \lesssim 0.01 ) rich galaxy clusters , perhaps in the form of a \sim 5 - 10 \mbox { Mpc } diameter ring-like emission tracing the cluster accretion shock , with luminous peaks at its intersections with galaxy filaments detectable even at z \simeq 0.025 .