Ultra High Energy Neutrinos: Absorption, Thermal Effects and Signatures
  We study absorption of ultra high energy neutrinos by the cosmic neutrino
background, with full inclusion of the effect of the thermal distribution of
the background on the resonant annihilation channel. For a hierarchical
neutrino mass spectrum (with at least one neutrino with mass below $\sim
10^{-2}$ eV), thermal effects are important for ultra high energy neutrino
sources at $z \gtrsim 16$. The neutrino transmission probability shows no more
than two separate suppression dips since the two lightest mass eigenstates
contribute as a single species when thermal effects are included. Results are
applied to a number of models of ultra high energy neutrino emission.
Suppression effects are strong for sources that extend beyond $z \sim 10$,
which can be realized for certain top down scenarios, such as superheavy dark
matter decays, cosmic strings and cosmic necklaces. For these, a broad
suppression valley should affect the neutrino spectrum at least in the energy
interval $10^{12} - 10^{13}$ GeV -- which therefore is disfavored for ultra
high energy neutrino searches -- with only a mild dependence on the neutrino
mass spectrum and hierarchy. The observation of absorption effects would
indicate a population of sources beyond $z \sim 10$, and favor top-down
mechanisms; it would also be an interesting probe of the physics of the relic
neutrino background in the unexplored redshift interval $z \sim 10 -100$.
