  Gravitational chiral anomaly connects the topological charge of spacetime and
the chirality of fermions. It has been known that the chirality is carried by
the particles (or the excited states) and also by vacuum. While the
gravitational anomaly equation has been applied to cosmology, distinction
between these two contributions has been rarely discussed. In the study of
gravitational leptogenesis, for example, lepton asymmetry associated with the
chiral gravitational waves sourced during inflation is evaluated only by
integrating the anomaly equation. How these two contributions are distributed
has not been seriously investigated. Meanwhile, a dominance of vacuum
contribution is observed in some specific types of Bianchi spacetime with
parity-violating gravitational fields, whose application to cosmology is not
straightforward. One may wonder whether such a vacuum dominance takes place
also in the system with chiral gravitational waves around the flat background,
which is more suitable for application to realistic cosmology. In this work, we
apply an analogy between U(1) electromagnetism and the weak gravity to the
spacetime that resembles the one considered in the gravitational leptogenesis
scenario. This approach allows us to obtain intuitive understanding of the
fermion chirality generation under the parity-violating spin-2 gravitational
field. By assuming the emergence of Landau level-like dispersion relation in
our setup, we conjecture that level-crossing does not seem to be efficient
while the charge accumulation in the vacuum likely takes place.
Phenomenological implication is also discussed in the context of gravitational
leptogenesis.
