Gravitational Baryogenesis from Entropy Production and Parity Violation: A Unified Framework

TL;DR

This work addresses the baryon asymmetry problem by proposing a unified gravitational baryogenesis framework that combines an entropy-production driven chemical potential with CP violation from a gravitational $\theta$-term, complemented by a dilaton-based UV completion. A minimal UV setup yields a sign-definite entropy clock with $Y_B \approx c\,\kappa\,\Pi_{\rm eff}$, while CP violation arises from $\epsilon_{\rm eff}=\kappa_{\rm inst}\,\theta$, with $\kappa_{\rm inst}$ in the $10^{-2}$–$10^{-1}$ range; the total yield is $Y_B = c\,\kappa\,\Pi_{\rm eff}\,\kappa_{\rm inst}\,\theta$. The framework predicts a testable gravitational-wave polarization signature $|\Pi| = \tanh(\pi\theta)$ for horizon-crossing modes in LQC bounces, reducing to $|\Pi| \approx \pi|\theta|$ for small $|\theta|$, with LISA-Taiji sensitivity potentially constraining $|\theta|$ at the $10^{-2}$–$10^{-3}$ level. By linking reheating history, high-scale parity violation, and entropy production, the approach provides a concrete path to connect baryogenesis with observable GW signatures and high-energy UV physics at $f_{\sigma} \sim 10^{17}$–$10^{18}$ GeV.

Abstract

We present a unified framework for gravitational baryogenesis combining two mechanisms: (i) an entropy-clock source that generates a sign-definite baryon chemical potential mu_B proportional to d ln S/dt during irreversible entropy production, and (ii) CP violation from a gravitational theta term theta R Rtilde analogous to the QCD vacuum angle. The entropy-clock evades adiabatic cancellation that suppresses purely oscillatory chemical potentials under smooth freeze-out; we quantify this with a universal low-pass transfer function F(x)=1/sqrt(1+x^2), where x=omega*tau_off. A minimal UV completion via a dilaton coupled to the conformal anomaly yields the entropy-clock coupling with decay constant f_sigma ~ 10^17-10^18 GeV. The theta term provides CP violation through interference between topologically distinct gravitational configurations; we estimate an instanton suppression factor kappa_inst ~ 10^-2-10^-1. The combined mechanism predicts Y_B ~ c*kappa*Pi_eff*epsilon_eff, linking the baryon asymmetry to the reheating temperature, the theta angle, and the entropy-production history. For Loop Quantum Cosmology bounces we derive an analytic expression for the circular polarization of the stochastic gravitational-wave background, with |Pi| ~ pi*|theta| for horizon-crossing modes, potentially testable by future space-based detectors.

Figures (5)

• Figure 1: Universal low-pass transfer function $F(x)=1/\sqrt{1+x^2}$ controlling the suppression of purely oscillatory (zero-mean) chemical potentials under smooth freeze-out, with $x\equiv\omega\tau_{\rm off}$.
• Figure 2: Predicted circular polarization fraction $\Pi=\tanh(\pi\theta)$ for horizon-crossing modes in the LQC bounce approximation. For $|\theta|\ll1$ the relation is linear, $|\Pi|\simeq\pi|\theta|$.
• Figure 3: Ratio $|\Pi|/(\pi|\theta|)$ quantifying the accuracy of the linear approximation $|\Pi|\simeq\pi|\theta|$. The deviation remains within ${\cal O}(10\%)$ for $|\theta|\lesssim 0.1$.
• Figure 4: Parameter space in the $(\theta, \kappa)$ plane for fixed $\kappa_{\rm inst} = 0.05$ and $\Pi_{\rm eff} = 1$. The blue band shows the region yielding $Y_B = (8.6 \pm 0.1) \times 10^{-11}$. The red region is excluded by current bounds on $\theta$ from gravitational wave observations. The green dashed line indicates the LISA-Taiji sensitivity threshold $|\theta| = 0.006$.
• Figure 5: Parameter space in the $(f_\sigma, T_{\rm rh})$ plane. The blue band corresponds to successful baryogenesis with $Y_B \simeq 8.6 \times 10^{-11}$. The orange region is excluded by the gravitino bound $T_{\rm rh} \lesssim 10^{10}$ GeV in gravity-mediated SUSY. The purple region indicates $f_\sigma > M_{\rm Pl}$, requiring trans-Planckian physics.