  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.
