Constraints on the VHE Emissivity of the Universe from the Diffuse GeV   Gamma-Ray Background
  VHE (Very High Energy, E>100 GeV) radiation emitted at cosmological distances will pair produce on low-energy diffuse extragalactic background radiation before ever reaching us. This prevents us from directly seeing most of the VHE emission in the Universe. However, a VHE gamma-ray that pair produces initiates an electromagnetic pair cascade. At low energies, this secondary cascade radiation has a spectrum insensitive to the spectrum of the primary gamma-radiation and, unlike the original VHE radiation, IS observable. Motivated by new measurements of the extragalactic MeV-GeV diffuse gamma-ray background, we discuss the constraints placed on cosmological VHE source populations by requiring that the cascade background they produce not exceed the observed levels. We use a new, accurate cascading code and pay particular attention to the dependence of the constraints on the diffuse cosmic background at infrared/optical wavelengths. Despite considerable uncertainty in this background, we find that robust constraints may still be placed on the integrated emissivity of potential VHE sources in the Universe. The limits are tighter than those obtained by considering cascading on the microwave background alone and restrict significantly, for example, the parameter space available for the exotic particle physics scenarios recently proposed to explain the highest energy cosmic ray events. If direct emission from blazar AGN in fact accounts for most of the observed GeV background, these limits strengthen and rule out AGN emission scenarios which produce significant power above 300 GeV. 
P.S. Coppi (1) and F.A. Aharonian (2) ((1) Yale University, (2)   Max-Planck-Institut fuer Kernphysik)