Reheating-temperature independence of cosmological baryon asymmetry in Affleck-Dine leptogenesis

In this paper we point out that the cosmological baryon asymmetry in our universe is generated almost independently of the reheating temperature $T_R$ in Affleck-Dine leptogenesis and it is determined mainly by the mass of the lightest neutrino, $m_{\nu_1}$, in a wide range of the reheating temperature $T_R\simeq 10^5$--$10^{12}$ GeV. The present baryon asymmetry predicts the $m_{\nu_1}$ in a narrow region, $m_{\nu_1}\simeq (0.3$--$1)\times 10^{-9}$ eV. Such a small mass of the lightest neutrino leads to a high predictability on the mass parameter $m_{\nu_e \nu_e}$ contributing to the neutrinoless double beta decay. We also propose an explicit model in which such an ultralight neutrino can be naturally obtained.