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^μ, ∂_μRJ^μ and proposed a mechanism for baryogenesis, the gravitational baryogenesis. Generally, however, ∂_μR vanishes in the radiation-dominated era. In this paper we consider a generalized form of their interaction ∂_μf(R)J^μ and study again the possibility of gravitational baryo(lepto)genesis. Taking f(R)~lnR, we will show that ∂_μf(R)~∂_μR/R does not vanish and the required baryon number asymmetry can be naturally generated in the early universe.