A Model of Gravitational Leptogenesis

TL;DR

The paper analyzes radiatively-induced gravitational leptogenesis (RIGL), where two-loop gravitational corrections in curved spacetime generate a lepton asymmetry in the early universe within a minimal see-saw framework with heavy Majorana neutrinos of order $10^{10}$ GeV. It derives an effective action containing CP-even and CP-odd curvature couplings, introduces a curvature-driven chemical potential $\mu = b\dot{R}$, and extends the Boltzmann equations to track the lepton asymmetry under gravity alongside standard Lagrangian processes. The analysis shows that gravitational terms can drive the asymmetry to the observed baryon-to-photon ratio after sphaleron conversion in realistic parameter regimes, and it explores how the outcome depends on neutrino Yukawa phases, mass hierarchies, and cosmological histories (e.g., varying $w$ or kination-era reheating). Overall, the work highlights the nontrivial role of quantum effects in curved spacetime for generating cosmological matter-antimatter asymmetry and provides a framework for evaluating RIGL across parameter space and cosmological scenarios.

Abstract

Gravitational leptogenesis is an elegant way of explaining the matter-antimatter asymmetry in the universe. This paper is a review of the recently proposed mechanism of radiatively-induced gravitational leptogenesis (RIGL), in which loop effects in QFT in curved spacetime automatically generate an asymmetry between leptons and antileptons in thermal quasi-equilibrium in the early universe. The mechanism is illustrated in a simple see-saw BSM model of neutrinos, where the lepton-number violating interactions required by the Sakharov conditions are mediated by right-handed neutrinos with Majorana masses of O(10^10) GeV. The Boltzmann equations are extended to include new, loop-induced gravitational effects and solved to describe the evolution of the lepton number asymmetry in the early universe. With natural choices of neutrino parameters, the RIGL mechanism is able to generate the observed baryon-to-photon ratio in the universe today.

Figures (10)

• Figure 1: Illustration of the key stages in the evolution of the lepton asymmetry $N_L(z)$ with temperature, given by the Boltzmann equation (\ref{['a6']}). The temperature dependence of the normalised rate factor $W(z)$ for the lepton-violating reactions, which drive the asymmetry towards its equilibrium value $N_L^{eq}(z)$, is $W(z) \sim 1/z^2$, while both the gravitationally-induced terms $N_L^{eq}(z)$ and $\mathcal{W}(z)$ fall off as $1/z^5$.
• Figure 2: Feynman diagrams for the $\Delta L=2$ lepton number violating reactions $\nu_L~H \leftrightarrow \nu_L^{\,c}~ H$ and $\nu_L~\nu_L \leftrightarrow H ~H$, mediated by the 'charge violating' $\langle\, \nu_R ~~ \overline{\nu_R^{\,\,c}}\,\rangle$ propagator $S_\alpha^\times$.
• Figure 3: One-loop self-energy diagram for the light $\nu_L$ neutrinos with an intermediate charge-conserving $\nu_R$ propagator $S$. The fields at the vertices are shown explicitly for comparison with the Lagrangian (\ref{['b1']}).
• Figure 4: Two-loop self-energy diagrams for the light $\nu_L$ neutrinos giving rise to a lepton-antilepton asymmetry in curved spacetime.
• Figure 5: Diagrams for the decay $\nu_R^{\,\alpha} \rightarrow \nu_L^{\, i} \, H$ which contribute to the decay rate asymmetry factor $\varepsilon_\alpha$. At $O(\lambda^4)$ the relevant contribution to the $\Gamma(\nu_R\rightarrow\nu_L\,H)$ decay rate arises from the interference of the tree and one-loop diagrams shown. Similar diagrams, where the $S_\alpha$ and $S_\alpha^\times$ type $\nu_R$ propagators are switched compared to the figure, give the decay rate for $\nu_R^{\,\alpha} \rightarrow \nu_L^{\, i\, c}\, H$.