Matter-antimatter asymmetry in a rotating universe: Dirac spinors in axisymmetric Bianchi IX cosmology

The standard $Λ$CDM model, based on a highly symmetric FLRW geometry, successfully explains many observations but faces unresolved issues, motivating the exploration of alternative cosmological frameworks. We investigate the influence of spacetime geometry on the matter-antimatter asymmetry of the Universe within the Bianchi IX cosmological model. Motivated by early-universe dynamics, potential contributions to cosmological angular momentum, and the axisymmetric Bianchi IX model's relevance to certain CMB anomalies, we formulate the Dirac field in this background. Starting with a Lagrangian formalism, we derive the Dirac equation and develop the harmonic analysis of spinor fields, extending previous treatments in the Mixmaster universe. We solve the Dirac equations for non-rotating and rotating axisymmetric Bianchi IX spacetimes using a fixed-background approximation. We find that spatial anisotropy induces spin-dependent energy splittings, while global rotation produces particle-antiparticle asymmetries in the energy spectra, effects absent in FLRW models. These results demonstrate that spacetime geometry alone can imprint nontrivial structure on particle spectra, suggesting that geometric effects may contribute to the matter-antimatter asymmetry.