Gravitational leptogenesis with kination and gravitational reheating

We revisit the gravitational leptogenesis scenario in which the inflaton is coupled to gravity by the Chern-Simons term and the lepton asymmetry is generated through the gravitational anomaly in the lepton number current during inflation. We constrain the possible model parameter space by requiring the absence of ghost modes below the Planck scale, which would suggest the breakdown of the effective theory, and evaluate the net baryon asymmetry for various reheating processes. We find that the mechanism with these requirements is insufficient to explain the observed baryon asymmetry of the Universe for standard reheating scenarios. We show that, however, with the kination scenario realized in e.g. the $k$- and G-inflation models, a sufficient baryon asymmetry can be generated within a feasible range of the model parameters.