Affleck-Dine leptogenesis with an ultralight neutrino

We perform a detailed analysis on Affleck-Dine leptogenesis taking into account the thermal effects on the dynamics of the flat direction field φ. We find that an extremely small mass for the lightest neutrino ν₁, m_ν110^-8 eV is required to produce enough lepton-number asymmetry to explain the baryon asymmetry in the present Universe. We impose here the reheating temperature after inflation TR to be TR10⁸ GeV to solve the cosmological gravitino problem. The required value of the neutrino mass seems to be very unlike the case since the recent SuperKamiokande experiments suggest the masses of the heavier two neutrinos ν₂ and ν₃ to be in a range of 10^-1--10^-3 eV. We also propose a model to avoid this difficulty based on the Peccei-Quinn symmetry, where the required neutrino mass can be as large as m_ν110^-4 eV.