Non-Thermal Leptogenesis

• Non-Thermal Leptogenesis is a baryogenesis mechanism where out-of-equilibrium decays of non-thermally produced heavy neutrinos generate a net lepton asymmetry.
• It leverages inflaton decay to generate right-handed neutrinos when the reheating temperature is below the neutrino mass scale, thereby suppressing thermal wash-out processes.
• Realistic models including SO(10) GUTs and 3-3-1 frameworks implement this mechanism to reconcile neutrino masses, CP violation, and cosmological observables like the CMB.

Non-Thermal Leptogenesis refers to a class of baryogenesis scenarios in which the lepton asymmetry is generated by right-handed neutrinos or other heavy states produced non-thermally, most often via the decay of the inflaton or other scalar fields at the end of inflation. In contrast to the standard “thermal leptogenesis,” where heavy states are created through high-temperature scatterings in the early Universe plasma, non-thermal mechanisms decouple the heavy-state production from the thermal bath, allowing successful baryogenesis at lower reheating temperatures and evading several cosmological constraints.

1. Fundamental Mechanism and Dynamical Origins

Non-thermal leptogenesis exploits out-of-equilibrium decays of heavy states whose abundances originate from non-thermal processes, especially the decay of the inflaton or other scalars after inflation. A prototypical realization (Fukuyama et al., 2010, Zhang, 2023, Zhang, 27 Jan 2025, Ghoshal et al., 2022) involves the superpotential or Lagrangian coupling: $$\mathcal{L} \supset y_N \phi N N + Y_\nu \bar{\ell}_L \tilde{H} N + \mathrm{h.c.}$$ where $\phi$ is the inflaton with mass $m_\phi$, $N$ is a heavy right-handed (RH) Majorana neutrino, and $Y_\nu$ is the Dirac Yukawa coupling.

After inflation, as the inflaton field oscillates and decays, the partial width for inflaton decay to RH neutrino pairs is generically: $$\Gamma(\phi \to N N) = \frac{y_N^2}{8\pi} m_\phi \left(1-\frac{4M_N^2}{m_\phi^2}\right)^{3/2}$$ where $M_N < m_\phi/2$ ensures kinematic accessibility. The crucial assumption is $M_N > T_R$ (reheating temperature), so thermal production and wash-out processes are exponentially suppressed.

Produced RH neutrinos decay via $N\to\ell H$, violating lepton number by two units in the presence of the Majorana mass and, through loop-induced CP violation, generate a net lepton asymmetry $\epsilon$, which is then partially recycled to baryon asymmetry via sphaleron transitions. For each species, the lepton asymmetry per decay is: $$\epsilon_i = -\frac{1}{2\pi (Y_\nu Y_\nu^\dagger)_{ii}} \sum_{j\ne i} \operatorname{Im}\left[(Y_\nu Y_\nu^\dagger)_{ij}^2\right] f\left(\frac{M_j^2}{M_i^2}\right)$$ with model-dependent loop function $f(x)$.

The produced baryon-to-entropy ratio is typically: $$\frac{n_B}{s} = -\frac{10}{31} \cdot \frac{3}{2} \sum_i \mathrm{BR}(\phi \to N_i N_i) \left(\frac{T_R}{m_\phi}\right) \epsilon_i$$ where $T_R$ is related to the total decay width by

$$T_R = \left(\frac{45}{4\pi^3 g_*}\right)^{1/4} \sqrt{\Gamma_{\mathrm{tot}} M_\mathrm{Pl}}$$

and $g_*$ is the effective number of relativistic degrees of freedom (Fukuyama et al., 2010).

2. Distinction from Thermal Leptogenesis and Parameter Impact

Unlike thermal leptogenesis, where wash-out processes severely limit the parameter space for successful baryogenesis (notably requiring $T_R \gtrsim 10^9$ GeV), non-thermal leptogenesis is highly efficient when $M_N > T_R$ and inflaton decay is the dominant production mode for heavy states (Fukuyama et al., 2010, Abdallah et al., 2012, Zhang, 2023). The lower $T_R$ reduces both wash-out and possibly problematic relic production (such as gravitinos in supersymmetric extensions).

Key parameters and their impacts are summarized as follows:

Parameter	Role/Constraint	Example Values/Relationships
$M_N$ (RHN mass)	Determines decay kinematics, seesaw scale	$M_N > T_R$, often $10^{6-14}$ GeV
$T_R$	Reheating temperature; must be $\ll M_N$	$T_R \sim 10^{6-10}$ GeV (model-dependent)
Inflaton mass, $m_\phi$	Sets kinematic ceiling for RHN production	$m_\phi > 2 M_N$
CP asymmetry, $\epsilon$	Magnitude fixed by model and Yukawa structure	Model-dependent (typically $10^{-6}$–$10^{-3}$)
Branching ratio, BR	Fraction of inflaton decays to RHN	$\mathcal{O}(1)$ is efficient

The effectiveness depends crucially on the ordering of scales, kinematics, and the structure of the seesaw sector.

3. Realizations in Grand Unified and Extended Models

Many realistic models implement non-thermal leptogenesis within GUT or extended symmetry frameworks. A canonical example is a supersymmetric SO(10) GUT in five dimensions (Fukuyama et al., 2010), where the decay chain proceeds:

1. SO(10) symmetry is broken on an orbifold down to the Pati–Salam group; all matter/Higgs fields reside on the Pati–Salam brane.
2. Smooth hybrid inflation ends with the inflaton decaying into scalar right-handed neutrinos.
3. Dirac Yukawa couplings $Y_\nu$ are fixed unambiguously (see Eq. (2) in (Fukuyama et al., 2010)) via fits to charged fermion data.
4. Tri-bimaximal neutrino mixing is assumed for $U_\mathrm{MNS}$, fixing the high-energy structure.
5. The correct baryon asymmetry $n_B/s \simeq 0.87 \times 10^{-10}$ is generated only for a normal neutrino mass hierarchy with the lightest eigenvalue $m_0 \simeq 1.8 \times 10^{-3}$ eV; for the inverted hierarchy, CP asymmetry and branching structure are ineffective (baryon asymmetry is too small).

Other constructions include supersymmetric 3-3-1 models, minimal seesaw with the “neutrino option” (Samanta et al., 2020), and $U(1)_{B-L}$ extensions (Ahmed et al., 2022), each exploiting the same inflaton-to-RHN non-thermal production route, while differing in their implementation of neutrino mass and CP-violating structures.

4. Efficiency, Wash-Out, and Flavor Effects

The efficiency of asymmetry transfer is significantly higher in non-thermal leptogenesis due to suppressed wash-out. In regimes where the inflaton decays rapidly but RHN decay is slower, a heavy-neutrino-dominated phase may occur (“RHN dominance”); if the RHNs decay immediately, “instantaneous reheating” applies; low $K$ (decay parameter) regions robustly avoid thermalization and wash-out (Zhang, 2023).

For $K$ (defined as $K = \Gamma_N / H$ at $T = M_N$) in the oscillation-preferred range ($K \sim 10$), a “strongly non-thermal” scenario persists (RHNs produced too sparsely to thermalize), keeping wash-out negligible even for moderate to large $Y_\nu$. This expands viable parameter space, possibly reducing the lower bound on $M_N$ to $2 \times 10^7$ GeV (or lower with flavor effects) for $T_R \geq 10^3$ GeV.

Flavor effects further enhance prospects. Once the charged-lepton Yukawa interactions equilibrate, each flavor asymmetry must be tracked. For two-flavor regimes (e.g., $\tau$ and $\tau^\perp$), the lower limit on RHN mass for successful leptogenesis can decrease (by factors $\sim$2–3). Boltzmann equations can be solved in fully flavored regimes for precise yield predictions (Zhang, 2023).

5. Connection to Inflationary Dynamics and Cosmological Observables

Non-thermal leptogenesis plausibly links baryogenesis to inflationary scenarios. If the inflaton is itself a field responsible for lepton-number breaking (Majoron or a scalar singlet), the inflation potential (Coleman–Weinberg or natural inflation) can be matched to current CMB data (Zhang, 2023, Zhang, 27 Jan 2025, Ghoshal et al., 2022). In such unified setups:

• The reheating process (“neutrino reheating”) is dictated by the decay chain $\phi\to N N$, followed by $N\to\ell H$ decay, with reheating temperature directly determined by the underlying couplings and inflaton mass (Zhang, 27 Jan 2025).
• The baryon asymmetry scales as $Y_B = (3/2) c_{sph} \epsilon (T_R / m_\phi)$ or, if RHN-dominated, $Y_B = (3/4) c_{sph} \epsilon (T_*/M_N)$, with $c_{sph}$ the sphaleron conversion factor.
• The duration and efficiency of reheating directly impact the mapping between the inflationary spectral index $n_s$, tensor-to-scalar ratio $r$, and $Y_B$, providing a new constraint to distinguish among models in the $(n_s, Y_B)$ or $(n_s, r)$ plane (Ghoshal et al., 2022, Zhang, 27 Jan 2025).

6. Robust Constraints and Observational Implications

Non-thermal leptogenesis scenarios introduce several non-trivial, testable implications:

Constraint/Implication	Origin/Mechanism
Lower $T_R$ for BAU	Wash-out suppressed (no thermal RHN production)
Allowed $M_N$ down to $2\times 10^7$ GeV (or lower)	Strongly non-thermal RHN scenario, even for moderate $K$
Baryon asymmetry traces $T_R/m_\phi$	Asymmetry scales with reheating temperature and inflaton mass
Neutrino hierarchy sensitivity	BAU successful only for normal hierarchy in models with fixed $Y_\nu$ (Fukuyama et al., 2010)
Inflation-CMB correlations	$(n_s, r)$ region narrowed by requirement of successful leptogenesis (Zhang, 27 Jan 2025)
Gravitino/minimal dark matter constraints	Lower $T_R$ relaxes BBN/gravitino overproduction bounds

Observational prospects include correlations between baryon asymmetry and inflationary signatures in the CMB, and potential gravitational wave imprints from inflation or cosmic strings coincident with the reheating scale (Ghoshal et al., 2022, Ahmed et al., 2022).

7. Theoretical Assumptions and Model Dependencies

Implementations of non-thermal leptogenesis rest on a set of assumptions:

• Heavy neutrino (or scalar triplet) masses $M_i$ satisfy $M_i > T_R$ to suppress thermal wash-out (Fukuyama et al., 2010).
• Coupling constants (inflaton–RHN, $\lambda$ or $y_N$) and the scales of inflation (inflaton mass, symmetry-breaking vev, etc.) must enable efficient production but not conflict with cosmological constraints (e.g., overproduction of relics).
• The form of the neutrino mass matrices and mixing is usually fixed by underlying GUT or flavor models (as in explicit $Y_\nu$ fits from SO(10) (Fukuyama et al., 2010)).
• In supersymmetric scenarios, the gravitino mass is taken heavy ($m_{3/2} \gtrsim 100$ TeV), accommodating substantial $T_R$ without BBN conflict (Fukuyama et al., 2010).

Specific model structures (e.g., texture zeros in RHN mass matrices, presence of PQ symmetry, extension to dark matter sectors) further tailor dynamics and phenomenology, while the outlined mechanism remains robust against a range of high-scale completions.

---

Non-thermal leptogenesis provides an extremely flexible and efficient framework for explaining the observed baryon asymmetry at scales compatible with neutrino mass models, inflationary physics, and cosmological constraints. Its predictive power stems from a close interconnection of high-scale dynamics (inflation, reheating) with low-energy observables and cosmological parameters, offering promising pathways for future experimental and observational tests.