Neutrino mass eigenvalues (solid lines) and one-third of the cosmologically relevant sum of the three neutrino mass eigenvalues (dashed line) as a function of the smallest neutrino mass eigenvalue for normal hierarchy (left) and inverted hierarchy (right). The upper limit from the tritium -decay experiments at Mainz and Troitsk on (solid line), which holds in the degenerate neutrino mass region for each , and for (dashed line) is also marked. We plot here the third of the sum of the neutrino mass eigenstates because it coincides with the mass of the individual neutrino mass states in the case of quasi-degenerate neutrino masses (for eV). The temperature of the cosmic microwave background photons together with the different decoupling times of the relic photons and the relic neutrinos after the big bang yields a relic neutrino density of 336/cm3 [6]. Using this number, the hot dark matter contribution of neutrinos to the matter/energy density of the universe relates directly to the average neutrino mass . This hot dark matter component is indicated by the right scale of the normal hierarchy plot and compared to all other known matter/energy contributions in the universe (middle). Thus, the laboratory neutrino mass limit from tritium -decay eV corresponds to a maximum allowed neutrino matter contribution in the universe of .
