Gravitational leptogenesis and neutrino mass limit

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