Search for the Cosmic Neutrino Background and KATRIN

The spectrum of the Cosmic Microwave Background follows Planck's black body radiation formula and shows a remarkable constant temperature of T = 2.7. About 380 000 years after the Big Bang at a temperature of T = 3000 Kelvin in the matter dominated era the electrons combine with the protons and 4He and the photons move freely in the neutral universe. So the temperature and distribution of the photons give us information of the universe 380 000 years after the Big Bang. Information about earlier times can, in principle, be derived from the Cosmic Neutrino Background (relic neutrinos). The neutrinos decouple already about 1 second after the Big Bang at a temperature of around 1 MeV or 10^{10} Kelvin. Today their temperature is about 1.95 Kelvin. Registration of these neutrinos is an extremely challenging experimental problem, which can hardly be solved with the present technologies. On the other hand it represents a tempting opportunity to check one of key elements of the Big Bang Cosmology and to probe the early stages of the universe evolution. The search for the Cosmic Neutrino Background with the induced beta decay: relic neutrino + 3H --> 3He + e-, is the topic of this contribution. The signal would show up as a peak in the electron spectrum by an energy with the neutrino mass above the Q value. We discuss the prospects of this approach and argue that it is able to set limits on the Cosmic Neutrino density in our vicinity. We also discuss critically ways to increase with modifications of the present KATRIN spectrometer the Tritium source intensity by a factor 100, which would yield about 170 counts of relic neutrino captures per year. Presently such an increase of the Tritium source intensity seems not to be possible. But one should be able to find an upper limit for the local density of the relic neutrinos in our galaxy.