Curvature and thermal corrections in tree-level CPT-Violating Leptogenesis

Abstract In a model for leptogenesis based on spontaneous breaking of Lorentz and $$\mathcal {CPT}$$ CPT symmetry [1–3], we examine the consistency of using the approximation of plane-wave solutions for a free spin-$$\frac{1}{2}$$ 12 Dirac (or Majorana) fermion field propagating in a Friedmann–Lema$$\hat{\mathrm{i}}$$ i^ tre–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).