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 $Φ$, CTE fixes the leading operators: a shift-symmetric derivative portal $((\partial_μΦ)J^μ_{B-L}/M_*)$ that acts as a dynamical chemical potential in FRW, and a topological term $(Φ\,R\tilde R)$ 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 $η_B$, tensor chirality $χ_T$, and the drift of $Φ$, together with a tri-observable relation that ties $η_B$ to cosmic birefringence $Δα$ and $χ_T$. 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.

Figures (5)

• Figure 1: CTE-locked geometric baryogenesis. The unique shift-symmetric portal $\mathcal{O}_1=(\partial_\mu\Phi/M_*)J^\mu_{B-L}$ yields $\mu_{B-L}=\dot\Phi/M_*$ and fixes the $B{-}L$ asymmetry at decoupling $T_D$. The parity-odd coupling $\mathcal{O}_2=(\Phi/f_\Phi)R\tilde{R}$ vanishes on homogeneous FRW but induces tensor birefringence and chirality $\chi_T$ for perturbations, implying the sign relation $\mathrm{sign}\,\eta_B=\mathrm{sign}\,\chi_T=\mathrm{sign}\,\dot\Phi$ (up to the convention for $\mu_g$).
• Figure 2: Slow-roll vs. resonant baryon yield as a function of the decoupling temperature $T_D$. Defaults: $g_*=106.75$, $S=16$ (SM$+$3$\nu_R$), $\xi=2.0$, $M_{\rm Pl}=1.22\times10^{19}\,\mathrm{GeV}$ (unreduced), and $\Phi_0/M_*=1200.0$. The gray band shows the observed yield $n_B/s \simeq (8.7\pm0.1)\times10^{-11}$ (using $\eta_B\simeq 6.1\times10^{-10}$ and $n_B/s\approx \eta_B/7.04$).
• Figure 3: Small-coupling domain for dynamical Chern-Simons parity effects. The shaded region satisfies $|\varepsilon_{\rm CS}|<10^{-3}$, consistent with Eq. \ref{['eq:CSbounds']}. The boundary is $\xi=\varepsilon_{\max} M_{\rm Pl}^2/(M_\ast \mu_g)$ with $\varepsilon_{\max}=10^{-3}$ and $M_\ast=10^{18}\,\mathrm{GeV}$. Benchmarks B1-B3 (Table \ref{['tab:benchmarks']}) lie safely inside.
• Figure 4: Tri-observable relation$\eta_B=\kappa_{\rm CTE}\,\chi_T\sin(2\Delta\alpha)$ with $\eta_B$ shown in units of $10^{-11}$. (a) Compressed variable $x=\chi_T\sin(2\Delta\alpha)$. (b) Fixed $\Delta\alpha$: straight lines in $\chi_T$ with slope $\kappa_{\rm CTE}\sin(2\Delta\alpha)$. (c) Fixed $\chi_T$: sinusoidal in $\Delta\alpha$ with amplitude $\kappa_{\rm CTE}\chi_T$. Gray bands: Planck; red dashed: bounds $|\chi_T|\le 0.1$, $|\Delta\alpha|\le 0.7^\circ$ (so $|x|\le 0.1\sin 0.7^\circ$).
• Figure 5: Freeze-out kernel and resonant capture. (a) Symmetric exponential window $W(t-t_D)$ weights an oscillatory bias $\mu_{B-L}(t)$. (b) The captured fraction is Lorentzian, $(1/2)/[1+(\omega/\Gamma_{\Delta L=2})^2]$, peaking at $1/4$ for $\omega=\Gamma_{\Delta L=2}$.