Cosmological Constraints on the Mass and the Number of Heavy Lepton Neutrinos

If the neutrinos associated with the heavy leptons have the masses, they may decay into the lower mass neutrinos. We discuss implications of the decays of those massive neutrinos in the standard big bang model of the universe and derive the constraints on their masses and the number from the cosmological observations, i.e., 1) the lower limit of the age of the universe and the upper limit of deceleration parameter, 2) the upper limit of the observed cosmic background radiation and 3) the upper limit of the primordial abundance of 4He. The following results are then obtained: 1) No neutrinos should exist in the mass range 70 eV ≪ mν≪23 MeV. 2) If the muon and electron neutrinos are also massive, number of neutrinos lighter than 70 eV should be less than four. 3) A limit to the number of the neutrinos heavier than 23 MeV but ligher than 50 MeV is obtained as a function of the mass of neutrinos.