On the lepton number excitation in gravitational leptogenesis

Abstract

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. However, in the study of gravitational leptogenesis, for example, lepton asymmetry associated with the chiral gravitational waves sourced during inflation is conventionally evaluated only by integrating the anomaly equation. In this evaluation, no distinction between the excite states and vacuum contribution has been made.  In this talk, I apply an analogy between U(1) electromagnetism and the weak gravity to the spacetime that resembles the one considered in the gravitational leptogenesis scenario. By assuming the emergence of Landau level-like dispersion relation in our setup, I suggest that level-crossing does not seem to be efficient while the charge accumulation in the vacuum likely takes place. Phenomenological implication is also discussed.

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