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A suppression in the spectrum of ultrahigh-energy (UHE, >= 10^{18} eV) neutrinos will be present in extra-dimensional scenarios, due to enhanced neutrino-antineutrino annihilation processes with the supernova relic neutrinos. In the n>4 scenario, being n the number of extra dimensions, neutrinos can not be responsible for the highest energy events observed in the UHE cosmic ray spectrum. A direct implication of these extra-dimensional interactions would be the absence of UHE neutrinos in ongoing and future neutrino telescopes.

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