For the first time the antineutrino spectrum formed as a result of neutron and tritium decays during the epoch of primordial nucleosynthesis is calculated. This spectrum is a non-thermal increase in addition to the standard cosmic neutrino background (C$ u$B) whose thermal spectrum was formed before the beginning of primordial nucleosynthesis. For energy larger than $10^{-2},$eV the calculated non-thermal antineutrino flux exceeds the C$ u$B spectrum and there are no other comparable sources of antineutrino in this range. The observations of these antineutrinos will allow us to look directly at the very early Universe and non-equilibrium processes taken place before, during, and some time after primordial nucleosynthesis.
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