Gravitational leptogenesis and neutrino mass limit

Recently Davoudiasl et al. (hep-ph/0403019) have introduced a new type of interaction between the Ricci scalar R and the baryon current $J^{\mu },$ ${\partial }_{\mu }{\mathrm{RJ}}^{\mu }$ and proposed a mechanism for baryogenesis, the gravitational baryogenesis. Generally, however, ${\partial }_{\mu }R$ vanishes in the radiation-dominated era. In this paper we consider a generalized form of their interaction ${\partial }_{\mu }{f\left(R\right)J}^{\mu }$ and study again the possibility of gravitational baryo(lepto)genesis. Taking $f\left(R\right)\mathrm{}\sim \ln R,$ we will show that ${\partial }_{\mu }f\left(R\right)\mathrm{}\sim {\partial }_{\mu }R/R$ does not vanish and the required baryon number asymmetry can be naturally generated in the early universe.