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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 enhancedneutrino-antineutrino annihilation processes with the supernova relicneutrinos. In the n>4 scenario, being n the number of extra dimensions,neutrinos can not be responsible for the highest energy events observed in theUHE cosmic ray spectrum. A direct implication of these extra-dimensionalinteractions would be the absence of UHE neutrinos in ongoing and futureneutrino telescopes.

Ultrahigh-energy neutrino flux as a probe of large extra-dimensions