Gravitational Leptogenesis and Neutrino Mass Limit

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