  The Pierre Auger Observatory for cosmic rays provides a laboratory for
studying fundamental interactions at energies well beyond those available at
colliders. In addition to hadrons or photons, Auger is sensitive to ultra-high
energy neutrinos in the cosmic radiation and models for new physics can be
explored by observing neutrino interactions at center-of-mass energies beyond
the TeV scale. By comparing the rate for quasi-horizontal, deeply penetrating
air showers triggered by all types of neutrinos with the rate for slightly
upgoing showers generated by Earth-skimming tau neutrinos, any deviation of the
neutrino-nucleon cross-section from the Standard Model expectation can be
constrained. We show that this can test models of low-scale quantum gravity
(including processes such as Kaluza-Klein graviton exchange, microscopic black
hole production and string resonances), as well as non-perturbative electroweak
instanton mediated processes. Moreover, the observed ratios of neutrino flavors
would severely constrain the possibility of neutrino decay.
