The Cosmic Microwave Background (CMB) yields information about our Universe
at around 380 000 years after the Big Bang (BB). Due to the weak interaction of
the neutrinos with matter the Cosmic Neutrino Background (CNB) should give
information about a much earlier time of our Universe, around one second after
the Big Bang. Probably the most promising method to see' the Cosmic Neutrino Background is the capture of the electron neutrinos from the Background by Tritium, which then decays into 3He and an electron with the energy of the the Q-value = 18.562 keV plus the electron neutrino rest mass. The KArlsruhe
TRItium Neutrino’ (KATRIN) experiment, which is in preparation, seems presently
the most sensitive proposed method for measuring the electron antineutrino
mass. At the same time KATRIN can also look by the reaction: electron neutrino
(~1.95 Kelvin) + 3H --> 3He + e- (with the energy Q = 18.6 keV + electron
neutrino mass). The capture of the Cosmic Background Neutrinos (CNB) should
show in the electron spectrum as a peak by the electron neutrino rest mass
above Q. Here the possibility to see the CNB with KATRIN is studied. A
detection of the CNB by KATRIN seems not to be possible at the moment. But
KATRIN should be able to determine an upper limit for the local electron
neutrino density of the CNB.

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