Intergalactic $gamma$-ray propagation: basic ideas, processes, and constraints

We review extragalactic $gamma$-ray propagation models with emphasis on the electromagnetic (EM) cascade process in the magnetized expanding Universe. We consider cascades initiated by primary protons of ultra-high energy accelerated by blazars and show that the observable spectrum is similar to the universal spectrum of a purely EM cascade. We also present a detailed calculation of the observable angular distribution for the case of EM cascades developing from relatively nearby (<20 Mpc) sources. Finally, we calculate the point-like source differential sensitivity of a novel liquid Argon time projection chamber $gamma$-ray telescope and show that its sensitivity is several times better than the Fermi LAT sensitivity in the 100 MeV -- 100 GeV energy range.