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The astrophysical neutrinos discovered by IceCube have the highest detected neutrino energies --- from TeV to PeV --- and likely travel the longest distances --- up to a few Gpc, the size of the observable Universe. These features make them naturally attractive probes of fundamental particle-physics properties, possibly tiny in size, at energy scales unreachable by any other means. The decades before the IceCube discovery saw many proposals of particle-physics studies in this direction. Today, those proposals have become a reality, in spite of astrophysical unknowns. We will showcase examples of doing fundamental neutrino physics at these scales, including some of the most stringent tests of physics beyond the Standard Model. In the future, larger neutrino energies --- up to tens of EeV --- could be observed with larger detectors and further our reach.
High-energy cosmic neutrinos can reveal new fundamental particles and interactions, probing energy and distance scales far exceeding those accessible in the laboratory. This white paper describes the outstanding particle physics questions that high-e
The astrophysical neutrinos recently discovered by the IceCube neutrino telescope have the highest detected neutrino energies --- from TeV to PeV --- and travel the longest distances --- up to a few Gpc, the size of the observable Universe. These fea
High-energy neutrinos, arising from decays of mesons that were produced through the cosmic rays collisions with air nuclei, form unavoidable background noise in the astrophysical neutrino detection problem. The atmospheric neutrino flux above 1 PeV s
Discovering neutrino decay would be strong evidence of physics beyond the Standard Model. Presently, there are only lax lower limits on the lifetime $tau$ of neutrinos, of $tau/m sim 10^{-3}$ s eV$^{-1}$ or worse, where $m$ is the unknown neutrino ma
This is a summary of a series of lectures on the current experimental and theoretical status of our understanding of origin and nature of cosmic radiation. Specific focus is put on ultra-high energy cosmic radiation above ~10^17 eV, including seconda