Can the negative mass square of the electron neutrino be an indication of degenerated relic neutrinos?

The unphysical result of the negative mass square of the electron neutrinos recently reported in several tritium β-decay experiments, is one of the most attractive subjects among remaining physical problems. As a possible scenario to explain the anomaly, we have assumed a reaction with relic neutrinos which are predicted by the standard big bang cosmology. If such neutrinos could exist, the interaction of the relic neutrinos with the target tritium, νe+3H→3He+e− could be laid under the large amount of the β-decay process, 3H→3He+e−+νē, which would cause a peak-like structure beyond the end-point in the Kurie plot. Based on the assumption, we evaluated the cross section from the event rate found in the peak by re-fitting to the 1991 data published by the Mainz Group. In this letter we will provide a scenario that can account for the evaluated cross section by introducing a spatially inhomogeneous neutrino degeneration, which would result much lower temperature than the prediction from the standard big bang cosmology.