  In a model for leptogenesis based on spontaneous breaking of Lorentz and CPT
symmetry [1-3], we examine the consistency of using the approximation of
plane-wave solutions for a free spin-(1/2) Dirac (or Majorana) fermion field
propagating in a Friedmann-Lemaitre-Robertson-Walker space time augmented with
a cosmic time-dependent (or, equivalently, a temperature-dependent) Kalb-Ramond
(KR) background. For the range of parameters relevant for leptogenesis, our
analysis fully justifies the use of plane-wave solutions in our study of
leptogenesis with Boltzmann equations; any corrections induced by
space-time-curvature are negligible. We also elaborate further on how the
lepton asymmetry is communicated to the Baryon sector. We demonstrate that the
KR background (KRB) does not contribute to the anomaly equations that determine
the baryon asymmetry a) through an explicit evaluation of a triangle Feynman
graph and b) indirectly, on topological grounds, by identifying the KRB as
torsion (in the effective string-inspired low energy gravitational field
theory).
