Recently Davoudiasl { \it et al} \cite{ steinhardt} have introduced a new type of interaction between the Ricci scalar $R$ and the baryon current $J^{ \mu}$, ${ \partial_\mu R} J^{ \mu}$ 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, $\partial_{ \mu}f(R)J^{ \mu}$ and study again the possibility of gravitational baryo(lepto)genesis. Taking $f(R)\sim \ln R$, we will show that $\partial_{ \mu}f(R)\sim \partial_{ \mu} R/R$ does not vanish and the required baryon number asymmetry can be { \it naturally} generated in the early universe.
Categories: hep-ph astro-ph gr-qc hep-th