Exploring Matter-Antimatter Asymmetry in a Rotating Universe

Abstract

This thesis investigates the potential role of spatial anisotropies and global rotation in addressing the observed matter-antimatter asymmetry in the universe. The standard cosmological model, ΛCDM, faces several unresolved puzzles, in- cluding CMB anomalies, dark matter, and the matter-antimatter asymmetry. The CMB anomalies suggest deviations from isotropy, prompting the exploration of more general anisotropic models. Additionally, current solutions to dark matter and matter- antimatter asymmetry imply the need for extensions beyond the Standard Model. Given these issues, it is crucial to question the accuracy of the FLRW geometry in ΛCDM. This thesis explores the rotating Bianchi IX universe, motivated by the BKL conjecture and the potential role of global rotation in cosmological angular momentum generation, in an effort to investigate the anisotropic effects of geometry on the particle spectrum. The Weyl and Dirac spinor fields are studied within the Bianchi IX universe, con- sidering a range of models, from the axisymmetric Bianchi IX universe to the more general rotating Bianchi IX model. The Hamiltonian for spinor fields in this back- ground is formulated, and the corresponding equations of motion for Weyl and Dirac spinors are derived. The field equations are solved in a fixed background as an initial step toward understanding the particle spectrum in such spacetimes. This approach sets the stage for future refinements using the adiabatic approximation and the WKB approximation. Generalized spinor spherical harmonics are obtained using analogies with the asymmetric “ideal” top. Building on previous work on the diagonal Bianchi IX model, we generalize this approach for spinor fields in a broader Bianchi IX framework. Our work builds on earlier studies of Weyl spinors and the phenomenon of level crossing, which results in the creation of neutrinos instead of antineutrinos in an ax- isymmetric Bianchi IX universe as the universe evolves toward isotropy. We extend this analysis to a broader class of models, examining how these effects manifest in more general rotating and anisotropic cosmological backgrounds. While Weyl fermions do not describe neutrinos in nature, the mathematical framework developed here is useful for analyzing the Dirac equations in this context. For Dirac fermions in the axisymmetric Bianchi IX model, we find that the energy spectrum is significantly influenced by the spin orientation, resulting in spin-dependent enhancements or suppressions for both particles and antiparticles. The inclusion of global rotation introduces further contributions due to the coupling between particle spin and the universe’s rotational motion. Specifically, rotational contributions to the energyspectrumcauseenergyshiftswithoppositeeffectsforparticlesandantiparticles. Depending on the alignment of the spin with the universe’s rotation, energy levels are either increased or decreased, leading to complex modifications in the energy structure. This spin-angular velocity coupling uncovers previously unexplored mechanisms that could contribute to the observed asymmetry between matter and antimatter—effects absent in homogeneous and isotropic models. Therefore, these results underscore the importance of background anisotropies in the search for an explanation of the matter-antimatter asymmetry and encourage fur- ther investigation in this direction. The next logical step in this research is to solve the equations in a time-dependent background, beginning with the adiabatic approx- imation and later employing the WKB approximation to account for more realistic conditions. Furthermore, the analysis could be extended to include interactions within quantum electrodynamics (QED), enabling the exploration of whether these geomet- ric effects influence particle creation and annihilation processes. These efforts could provide valuable insights into the role of geometric effects in fundamental interactions, contributing to our understanding of the mechanisms driving the matter-antimatter asymmetry in the Universe