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Nucleosynthesis and the Mass of the τ Neutrino — Erratum

(27 June 1996) In a recent Letter [1] we presented the first numerical treatment of the full set of Boltzmann equations for the evolution of an MeV Majorana τ neutrino in the early Universe and concluded that mass limits from Big Bang nucleosynthesis were significantly weakened compared to previous investigations. An error in our numerical code unfortunately invalidates the results. As noticed by several people [2] one should expect a strengthening rather than a weakening of earlier mass limits based on the integrated Boltzmann equation [3,4] because our inclusion of the full neutrino spectra should reduce the annihilation of high-momentum neutrinos, thereby permitting more τ neutrinos to survive. This is indeed the case as shown in the revised Fig. 1 [5]. Our neutrino distribution functions now differ less from kinetic equilibrium than found in [1]. A typical case for ντ is shown in Fig. 2. Deviations by a factor of 2 appear frequently when compared to a kinetic equilibrium distribution, fν = [exp ((E − μ)/T ) + 1] , with the same number density and T = Tγ, as often assumed, whereas the distribution is close to that of a kinetic distribution with T and μ determined by the numberand energy densities. The resulting νe and νμ distributions are still significantly heated relative to the standard case with a massless ντ . For eV-mass νμ or νe this changes the present day contribution to the cosmic density to Ωνh 2 = αmν/93.03eV with α = 1 for a massless ντ , and α =1.10(1.13), 1.09(1.14), 1.03(1.05), 1.01(1.02) for νe(νμ) for mντ =5, 10, 15, 20 MeV (h is the Hubbleparameter in units of 100km s Mpc). Later decay of ντ can further increase the value of α. Fig. 3 illustrates the consequences for Big Bang nucleosynthesis in terms of the equivalent number of massless neutrinos, Neq, needed to give a similar production of He at a baryonto-photon ratio η = 3× 10. The revised results with and without inclusion of the change