Majorana masses,photon gas heating and cosmological constraints on neutrinos

Non-vanishing Majorana masses generally lead to flavor-changing neutral currents in the neutrino sector. It is shown that when both right- and left-handed neutrinos have non-vanishing Majorana masses (M_R≠0 and M_L≠0), flavor-changing neutral currents could be as large as flavor-diagonal ones. However, when only right-handed neutrinos have non-vanishing Majorana masses (M_R≠0 but M_L=0), flavor-changing neutral currents are small. If M_R?D (Dirac masses), they are of $\text{O}\text{((}\text{D}\text{M}{}_{\mathrm{<mtext>R</mtext>}}\text{)}{}^2\text{)}$. If M_R?D, they are $\text{?(}\text{m}{}_{\mathrm{<mtext>L</mtext>}}\text{m}{}_{\mathrm{<mtext>H</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where m_L and m_H are masses of light and heavy neutrinos appearing in a flavor-changing process.By using these results we examine cosmological implications of non-vanishing flavor-changing neutral currents. Heavy neutrinos can decay into three light neutrinos at an appreciable rate by exchanging a Z-boson. It is demonstrated that owing to this decay mode, heavy neutrinos of mass larger than 70 keV but less than 2m_e give rise to no contradiction with the standard big bang cosmology in the most general case.We also show that if there exist heavy neutrinos of mass m_H2m_e, their decay at an early era of the universe induces photon gas heating, which alters Cowsik and McClelland's constraint on light neutrino masses to Σm_L < k · 100 eV with the sum running over all Majorana eigenstates. Here the constant k, representing the heating effect of the photon gas, is restricted by the deuterium abundance of the present universe. For instance, Σm_L < 240 eV for m_H ～ 25 MeV and the present baryon density = 3.4 × 10^?31 g · cm^?3.