Electromagnetic Radiation from Cosmic-Ray Scatterings on Relic Neutrinos

Cosmic-ray scatterings on the cosmic neutrino background induce a flux of gamma-rays and X-rays from boosted meson decays and charged lepton processes. Here we present the first estimate of this flux and its cumulative cosmological contribution. Confronting expectations with Fermi-LAT diffuse gamma-ray data, we find a limit on the cosmic neutrino background overdensity at the level of $\eta \lesssim 2 \times 10^{4}$ for a lightest neutrino mass of $m_{\nu}\gtrsim0.1$ eV, orders of magnitude stronger than current direct laboratory probes, and comparable to constraints on the cosmic neutrino background obtained with IceCube. We further show that X-ray synchrotron emission from cascade electron-positron pairs in intergalactic magnetic fields provides a complementary, albeit weaker, constraint. We discuss how anisotropic signatures and future gamma-ray data from CTA could further improve bounds on the relic neutrino overdensity, approaching in sensitivity the $\Lambda$CDM expected density.