![]() ![]() ![]() By numerical coincidence, the position of the ρ-resonance overlaps with the originally predicted peak of the Greisen-Zatsepin-Kuzmin (GZK) neutrino flux, which offers an enhanced effect at higher redshifts. This leads to a distinct absorption feature in the cosmogenic neutrino flux at an energy solely determined by the meson mass and the neutrino mass, apart from redshift. Depending on the lightest neutrino mass and the energy spectrum of the cosmogenic neutrino flux, a Standard Model vector meson (such as a hadronic ρ) resonance can be produced via νν¯ annihilation. We propose a new probe of cosmic relic neutrinos (CνB) using their resonant scattering against cosmogenic neutrinos. Using our results for the degenerate case, we also obtain the mean relic velocity of the recently proposed non-thermal cosmic neutrino background. We also compute the behavior of the phase space density under expansion and compare it to the case of real temperature and real chemical potential. This calculation is enabled by a new expansion of the Fermi-Dirac integral, which is for our purpose superior to the well-known Sommerfeld expansion. We find expressions for the effective temperature and effective chemical potential which allow us to calculate the final spectrum for arbitrary initial conditions. Assuming perpetual equilibration, we study a decoupled gas which is relativistic at decoupling and then is red-shifted until it becomes non-relativistic. In contrast, the spectrum of a decoupled massive and non-degenerate gas can only be described by an effective temperature if there are strong enough self-interactions such as to maintain an equilibrium distribution. In case the gas is massless and/or completely degenerate, the spectrum of the gas can be described by an effective temperature and/or an effective chemical potential, both of which scale down with the volume expansion. The behavior of a decoupled ideal Fermi gas in a homogeneously expanding three-dimensional volume is investigated, starting from an equilibrium spectrum.
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