Beta Decay and the Cosmic Neutrino Background

¹ Institute für Theoretische Physik der Universität Tübingen, D-72076 Tübingen, Germany
² Institute of Experimental and Applied Physics, Czech Tecnical University, Horská 3a/22, 12800 Prague, Czech Republic
³ Universidad Técnica Federico Santa María, Centro-Científico-Tecnológico de Valparaíso, Casilla 110-V, Valparaíso, Chile
⁴ JINR, 141980 Dubna, Moscow Region, Russia and Comenius University, Physics Dept., SK-842 15 Bratislava, Slovakia

^a e-mail: faessler@uni-tuebingen.de

Published online: 29 April 2014

Abstract

In 1964 Penzias and Wilson detected the Cosmic Microwave Background (CMB). Its spectrum follows Planck’s black body radiation formula and shows a remarkable constant temperature of T_0γ ≈ 2:7 K independent of the direction. The present photon density is about 370 photons per cm3. The size of the hot spots, which deviates only in the fifth decimal of the temperature from the average value, tells us, that the universe is flat. About 380 000 years after the Big Bang at a temperature of T_0γ = 3000 K already in the matter dominated era the electrons combine with the protons and the 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 (CνB). The neutrinos decouple already 1 second after the Big Bang at a temperature of about 10¹⁰ K. Today their temperature is ∼ 1:95 K and the average density is 56 electron-neutrinos per cm³. 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 the key element of the Big Bang cosmology and to probe the early stages of the universe evolution. The search for the CνB with the induced beta decay ν_e + ³H → ³He + e⁻ is the topic of this contribution. The signal would show up by a peak in the electron spectrum with an energy of 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 CνB density in our vicinity. We also discuss critically ways to increase with modifications of the present KATRIN spectrometer the source intensity by a factor 100, which would yield about 170 counts of relic neutrino captures per year. This would make the detection of the Cosmic Neutrino Background possible. Presently such an increase seems not to be possible. But one should be able to find an upper limit for the local density of the relic neutrinos (Cosmic Neutrino Background) in our galaxy.