Geometric Baryogenesis with Chiral-Time Equivalence

Abstract

The asymmetry between matter and antimatter demands a cause as simple as it is profound. Here we show that a single geometric principle Chiral-Time Equivalence (CTE)-suffices to generate and correlate the required CP violation with the time orientation of the cosmos. Promoting the Immirzi parameter to a pseudoscalar Nambu-Goldstone field $\Phi$, CTE fixes the leading operators: a shift-symmetric derivative portal $((\partial_\mu\Phi)J^\mu_{B-L}/M_*)$ that acts as a dynamical chemical potential in FRW, and a topological term $(\Phi\,R\tilde R)$ that imprints parity on tensor modes. In thermal equilibrium this structure produces gravity-assisted leptogenesis, whose magnitude is set at the decoupling temperature by susceptibilities rather than by tuned departures from equilibrium. A fully flavored Boltzmann network with curvature sources captures flavor transfer and washout, while slow-roll and resonant regimes are established via thermodynamic and Kubo formulas. Consistency is secured by an EFT analysis (stability, perturbative unitarity, and BBN safety), and by explicit elimination of EC torsion and control of dCS birefringence in the small-coupling domain. The most striking prediction is a sign locking among $\eta_B$, tensor chirality $\chi_T$, and the drift of $\Phi$, together with a tri-observable relation that ties $\eta_B$ to cosmic birefringence $\Delta\alpha$ and $\chi_T$. Thus a single, symmetry-protected geometric origin renders the baryon excess testable by TB/EB correlations and stochastic-wave chirality, and calculable within a minimal, ultraviolet-anchored effective theory.