We examine how light neutrinos coming from distant active galactic nuclei
(AGN) and similar high energy sources may be used as tools to probe
non-standard physics. In particular we discuss how studying the energy spectra
of each neutrino flavour coming from such distant sources and their distortion
relative to each other may serve as pointers to exotic physics such as neutrino
decay, Lorentz symmetry violation, pseudo-Dirac effects, CP and CPT violation
and quantum decoherence. This allows us to probe hitherto unexplored ranges of
parameters for the above cases, for example lifetimes in the range 10−3−104 s/eV for the case of neutrino decay. We show that standard
neutrino oscillations ensure that the different flavours arrive at the earth
with similar shapes even if their flavour spectra at source may differ strongly
in both shape and magnitude. As a result, observed differences between the
spectra of various flavours at the detector would be signatures of non-standard
physics altering neutrino fluxes during propagation rather than those arising
during their production at source. Since detection of ultra-high energy (UHE)
neutrinos is perhaps imminent, it is possible that such differences in spectral
shapes will be tested in neutrino detectors in the near future. To that end,
using the IceCube detector as an example, we show how our results translate to
observable shower and muon-track event rates.Comment: 16 pages, 10 figure
