  Recently, a new non-Standard Model neutrino interaction mediated by a light
scalar field was proposed, which renders the big-bang relic neutrinos of the
cosmic neutrino background a natural dark energy candidate, the so-called
Neutrino Dark Energy. As a further consequence of this interaction, the
neutrino masses become functions of the neutrino energy densities and are thus
promoted to dynamical, time/redshift dependent quantities. Such a possible
neutrino mass variation introduces a redshift dependence into the resonance
energies associated with the annihilation of extremely high-energy cosmic
neutrinos on relic anti-neutrinos and vice versa into Z-bosons. In general,
this annihilation process is expected to lead to sizeable absorption dips in
the spectra to be observed on earth by neutrino observatories operating in the
relevant energy region above 10^13 GeV. In our analysis, we contrast the
characteristic absorption features produced by constant and varying neutrino
masses, including all thermal background effects caused by the relic neutrino
motion. We firstly consider neutrinos from astrophysical sources and secondly
neutrinos originating from the decomposition of topological defects using the
appropriate fragmentation functions. On the one hand, independent of the nature
of neutrino masses, our results illustrate the discovery potential for the
cosmic neutrino background by means of relic neutrino absorption spectroscopy.
On the other hand, they allow to estimate the prospects for testing its
possible interpretation as source of Neutrino Dark Energy within the next
decade by the neutrino observatories ANITA and LOFAR.
