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Despite the spectacular discovery of an astrophysical neutrino flux by IceCube in 2013, its origin remains a mystery. Whatever its sources, we expect the neutrino flux to be accompanied by a comparable gamma-ray flux. These photons should be degraded in energy by electromagnetic cascades and contribute to the diffuse GeV–TeV flux precisely measured by the Fermi-LAT. Population studies have also permitted to identify the main classes of contributors to this flux, which at the same time have not been associated with major neutrino sources in cross-correlation studies. These considerations allow one to set constraints on the origin and spectrum of the IceCube flux, in particular its low-energy part. We find that, even accounting for known systematic errors, the Fermi-LAT data exclude to at least 95% C.L. any extragalactic transparent source class, irrespective of its redshift evolution, if the neutrino spectrum extends to the TeV scale or below. If the neutrino spectrum has an abrupt cutoff at ∼10 TeV, barely compatible with current observations, the tension can be reduced, but this way out requires a significant modification to the current understanding of the origin of the diffuse extragalactic gamma-ray flux at GeV energies. In contrast, these considerations do not apply if a sizable fraction of IceCube data originates within the Galactic halo (a scenario however typically in tension with other constraints) or from a yet unidentified class of “opaque” extragalactic emitters, which do not let the high-energy gamma rays get out.

A primordial black hole in the last stages of evaporation and located in the local neighborhood can produce a detectable signal in gamma ray and neutrino telescopes. We re-evaluate the expected gamma ray and neutrino fluxes from these transient point events and discuss the consequences for existing constraints. For gamma rays we improve the current bounds by a factor of few, while for neutrinos we obtain significantly different results than the existing literature. The capability and advantages of neutrino telescopes in the search for primordial black holes is discussed thoroughly. The correlations of gamma ray and neutrino energy and time profiles will be promoted as a powerful tool in identifying the primordial black holes, in case of detection.

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We study the impact of the muon pair production and double pair production processes induced by ultra-high energy photons on the cosmic microwave background. Although the muon pair production cross section is smaller than the electron pair production one, the associated energy loss length is comparable or shorter than the latter (followed by inverse Compton in the deep Klein-Nishina regime) at high-redshift, where the effect of the astrophysical radio background is expected to be negligible. By performing a simulation taking into account the details of e/γ interactions at high energies, we show that a significant fraction of the electromagnetic energy injected at E 10 19 eV at redshift z 5 is channeled into neutrinos. The double pair production plays a crucial role in enhancing the multiplicity of muon production in these electromagnetic cascades. The ultra-high energy neutrino spectrum, yet to be detected, can in principle harbour information on ultra-high energy sources in the young universe, either conventional or exotic ones, with weaker constraints from the diffuse gamma ray flux compared to their low redshift counterparts.