Quasar-driven outflows account for the missing extragalactic gamma-ray background

The origin of the extragalactic $\gamma$-ray background permeating throughout the Universe remains a mystery forty years after its discovery. The extrapolated population of blazars can account for only half of the background radiation at the energy range of ~ 0.1-10 GeV. Here we show that quasar-driven outflows generate relativistic protons that produce the missing component of the extragalactic $\gamma$-ray background and naturally match its spectral fingerprint, with a generic break above ~ 1 GeV. The associated $\gamma$-ray sources are too faint to be detected individually, explaining why they had not been identified so far. However, future radio observations may image their shock fronts directly. Our best fit to the Fermi-LAT observations of extragalactic $\gamma$-ray background spectrum provides constraints on the outflow parameters that agree with observations of these outflows and theoretical predictions.