Gravitational Leptogenesis and Neutrino Mass Limit

Abstract

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.

4 pages