Hunting for the cosmic neutrino background

We present the first comprehensive discussion of constraints on the cosmic neutrino background (CB) overdensity, including theoretical, experimental and cosmological limits for a wide range of neutrino masses and temperatures. Additionally, we calculate the sensitivities of future direct and indirect relic neutrino detection experiments and compare the results with the existing constraints, extending several previous analyses by taking into account that the CB reference frame may not be aligned with that of the Earth. The Pauli exclusion principle strongly disfavours overdensities at small neutrino masses, but allows for overdensities at the KATRIN mass bound . On the other hand, cosmology strongly favours in all scenarios. We find that direct detection proposals are capable of observing the CB without a significant overdensity for neutrino masses , but require an overdensity outside of this range. We also demonstrate that relic neutrino detection proposals are sensitive to the helicity composition of the CB, whilst some may be able to distinguish between Dirac and Majorana neutrinos.