Nonthermal Leptogenesis

• Nonthermal leptogenesis is defined as scenarios where heavy lepton-violating particles produced out of equilibrium decay to generate a net lepton asymmetry.
• It employs mechanisms such as inflaton or curvaton decays and first-order phase transitions to nonthermally produce heavy right-handed neutrinos while suppressing washout effects.
• This paradigm yields testable predictions including gravitational wave signals and collider signatures, linking baryogenesis to early Universe dynamics.

Nonthermal leptogenesis refers to a class of baryogenesis scenarios in which the lepton asymmetry responsible for the observed baryon asymmetry of the Universe is generated via mechanisms that do not rely on the thermal population of the relevant heavy particles in the early Universe plasma. Instead, lepton number–violating particles (such as heavy right-handed neutrinos, exotic scalars, or shadow fermions) are produced through nonthermal, out-of-equilibrium processes—such as inflaton decays, phase transitions, or bubble wall dynamics—and subsequently decay or annihilate to yield a lepton asymmetry. The mechanism is characterized by the combination of out-of-equilibrium particle production, lepton number and CP violation in decay or annihilation, and the essential avoidance or suppression of washout effects, thereby fulfilling the Sakharov conditions under dynamical, cosmological circumstances that are distinct from standard thermal leptogenesis.

1. Principles and General Mechanism

Nonthermal leptogenesis scenarios achieve the generation of a net lepton number through the out-of-equilibrium decay or annihilation of heavy particles whose population is produced by a mechanism other than thermal excitation. In contrast to thermal leptogenesis, where the relevant particles (typically Majorana neutrinos) are efficiently produced and equilibrated via Standard Model or extension-of-SM scatterings and inverse decays, nonthermal leptogenesis introduces an external production channel, most commonly:

• Decay of a cosmological scalar field (inflaton, curvaton, or axion-like field post-inflation): The heavy particles responsible for lepton number violation are produced via the decay of such fields after inflation or another era of cosmic acceleration (Fukuyama et al., 2010, Huong et al., 2010, Antusch et al., 2010, Fong et al., 2013, Fong et al., 2023).
• Dynamics of first-order phase transitions: Bubble nucleation and subsequent expansion, collisions, or wall-plasma interactions nonthermally populate heavy particles from the latent vacuum energy (Huang et al., 2022, Cataldi et al., 23 Jul 2024, Ai et al., 10 Oct 2025).
• Nonstandard couplings or time-dependent effective interactions: Mechanisms where neutrino or lepton-number–violating couplings switch on only after the Universe cools sufficiently, postponing both production and washout of the asymmetry (Huang et al., 2023).

The core sequence realized in these models is:

1. Nonthermal Production of L-violating particles X at rate $\sim \Gamma_{prod}$, yielding a number density $n_X$ out of equilibrium.
2. Decay or Annihilation of X via L- and CP-violating channels, with a CP asymmetry parameter $\epsilon$ determined by model-specific loop-induced or interference effects.
3. Partial Sphaleron Conversion of the net lepton number to baryon number in the presence of efficient electroweak sphaleron processes.
4. Suppression of Washout: Washout by inverse decays and scatterings is minimized because the bath temperature is much lower than the X mass or L-violating interactions only become effective at low temperatures.

The final baryon asymmetry is typically given by $Y_B \sim \epsilon \frac{n_X}{s} \kappa$, where $s$ is the entropy density and $\kappa$ encodes efficiency and possible suppression due to washout.

2. Nonthermal Production Mechanisms

Inflaton and Curvaton Decays

Inflaton decay post-inflation is a canonical example of nonthermal production. The inflaton decays into heavy right-handed (s)neutrinos or other relevant particles with rate $\Gamma_\phi$, leading to a nonthermal yield $$Y_N^0 \simeq BR(\phi \to NN) \frac{3 T_R}{4 M_\phi}$$, where $T_R$ is the reheating temperature and $M_\phi$ is the inflaton mass (Fukuyama et al., 2010, Huong et al., 2010, Antusch et al., 2010). The decay rate is typically much lower than the expansion rate at the time, ensuring out-of-equilibrium decays.

Curvaton or majoron decays can also nonthermally populate right-handed neutrinos at late times, with the decay epoch and abundance tuned to produce both the observed curvature perturbation (as in curvaton models) and the required lepton asymmetry (Fong et al., 2023).

Bubble-Driven and Phase Transition–Based Mechanisms

First-order phase transitions enable nonthermal particle production through rapid conversion of vacuum energy during bubble nucleation and collisions. Examples include:

• Bubble Wall Collisions: Collisions produce highly energetic quanta of heavy RHNs via the neutrino portal or analogous mechanisms (Cataldi et al., 23 Jul 2024). The energy available can far exceed both the plasma temperature and the symmetry-breaking scale, allowing production of RHNs with masses orders of magnitude above the ambient thermal bath.
• Bubble Wall Plasmonic Dynamics: Expansion of relativistic bubble walls in an "inverse electroweak phase transition" sweeps plasma leptons into the bubble and enables kinematically forbidden transitions to heavy vectorlike leptons due to loss of translation invariance and the energy boost from the wall (Ai et al., 10 Oct 2025).
• First-Order Phase Transition–Induced Mass Gaps: In U(1)$_{B-L}$ breaking, RHNs are massless in the symmetric phase and acquire large masses inside newly nucleated bubbles; rapid, non-equilibrium penetration followed by prompt decay generates lepton asymmetry (Huang et al., 2022).

Dynamical or Delayed Coupling Onset

Temperature-dependent couplings (e.g., Dirac Yukawa coupling of the lightest RHN to SM leptons) create a scenario where neither RHN decay nor washout are efficient at high temperatures. Only when the Universe cools (or after a scalar field transition) does the coupling grow, allowing decay in the regime where thermal washout is already Boltzmann suppressed (Huang et al., 2023).

3. CP Violation and Lepton Number Violation

The generation of a lepton asymmetry universally requires CP-violating (and lepton number–violating) decay or annihilation amplitudes. In nonthermal leptogenesis, these arise through:

• Decay of Heavy Majorana Neutrinos: CP asymmetry induced by interference between tree-level and one-loop (vertex and self-energy) diagrams, with the canonical parameter

$$\epsilon_{i} = \frac{\Gamma_{i} - \overline{\Gamma}_{i}}{\Gamma_{i} + \overline{\Gamma}_{i}}$$

and one-loop contributions such as (Fukuyama et al., 2010)

$$\epsilon_i = -\frac{1}{2\pi (Y_\nu Y_\nu^\dagger)_{ii}}\sum_{j\ne i} \operatorname{Im} [(Y_\nu Y_\nu^\dagger)_{ij}^2] f(M_j^2/M_i^2)$$

with $f(x)$ a loop function.

• Scalar and Exotic Fermion Decays: Similar loop-induced CP asymmetries are present in messenger scalar decays (0810.3341), scalar singlet decays (Gu et al., 2018), or in the decay of heavy Majorana or Dirac scalars with lepton-number–violating interactions (Heeck, 2013).
• Soft Leptogenesis: In supersymmetric scenarios, CP violation arises via soft SUSY-breaking terms (e.g., complex trilinear $A_\alpha$ terms and bilinear $B$ terms), which split sneutrino masses and allow a nonzero asymmetry even at zero temperature (“nonthermal $CP$ violation”) (Adhikari et al., 2015).
• Interference in Annihilation or Scattering: When the relevant process is not decay but rather annihilation (e.g., dark matter annihilation in a $U(1)_D$ model), CP asymmetry is generated by the interference between a tree-level and a loop-induced s-channel process with a resonance (e.g., Breit–Wigner resonance in the $Z_D$ propagator) (Chun et al., 2020).

The magnitude of the CP asymmetry, its dependence on loop-level phases, and the structure of the associated Yukawa couplings are model-dependent but are always central to determining the final baryon asymmetry.

4. Suppression of Washout and Out-of-Equilibrium Conditions

A haLLMark of nonthermal leptogenesis is that the production and decay of heavy L-violating states occur sufficiently far from equilibrium that the generated asymmetry is not erased by inverse processes. This is ensured by several dynamical regimes:

• Low Reheating Temperatures: When $T_R \ll M_N$, the number density of heavy RHNs in the plasma is negligible, and washout rates are Boltzmann suppressed by $e^{-M_N/T}$ (Fong et al., 2013). Decays of nonthermally produced RHNs dominate.
• Delayed Onset of Couplings: Couplings responsible for both decay and washout become large only at $T \ll M_N$, as in the dynamically coupled models (Huang et al., 2023).
• Ultraheavy RHN Production: When the nonthermally produced particle has $M_N \gg T_*$ (plasma temperature after transition or collision), washout is exponentially suppressed and the otherwise problematic inverse decay/scattering processes are ineffective (Cataldi et al., 23 Jul 2024).
• Bubble Wall Isolation: For phase transition–driven scenarios, the wall–plasma interactions are so rapid and localized that any generated L-asymmetry is not equilibrated before being transferred to baryons via sphalerons (Huang et al., 2022, Ai et al., 10 Oct 2025).

Quantitatively, the efficiency factor $\kappa$ entering $Y_B$ can approach unity, in contrast to thermal leptogenesis where it is typically $\sim 10^{-2}$ in the strong washout regime (Huang et al., 2023).

5. Model Realizations and Theoretical Structures

Nonthermal leptogenesis mechanisms appear in a wide variety of BSM frameworks:

Class of Model	Nonthermal Production Mechanism	Washout Suppression	Key Observables
Inflaton/Curvaton Decay	Inflaton → RHN (out-of-eq. decay)	$T_R \ll M_N$	$n_B/s$, $n_s$, $f_{NL}$
Phase Transition–based	Bubble wall induces heavy state prod.	$M_N \gg T_*, v_\phi$	GWs, collider signals
Soft/Resonant Leptogenesis	Sneutrino mass mixing/soft terms	$T \lesssim 10^9$ GeV	LFV processes, EDMs
Dynamical Couplings	Yukawa switches on at low T	Washout "kicks in" late	Gravitational waves
Exotic Sectors (e.g., SU(2)$_Z$)	Shadow fermion/axion model	Model-specific	DE/DM unification

Significant examples include:

• Shadow Sector/Instanton Models: Lepton asymmetry from decays of Majorana shadow fermions in an SU(2)$_Z$ sector; simultaneous explanation of dark energy and dark matter (0810.3341).
• Minimal SO(10) and SU(3) × SU(3) × U(1): Inflaton-induced nonthermal RHN production, detailed connections to high-scale unification and precision constraints from cosmology (Fukuyama et al., 2010, Huong et al., 2010).
• TeV-scale Vectorlike Leptons and Inverse Seesaw: Testable models with phase transition–driven leptogenesis, inverse seesaw mechanism, and LHC signatures (Ai et al., 10 Oct 2025).
• Majoron Curvaton–Induced Leptogenesis: Simultaneous sourcing of density perturbations (curvaton), RHN nonthermal production, and leptogenesis, with primordial $f_{NL}$ as a probe (Fong et al., 2023).
• Models With Additional Higgs Doublets: Flavor and resonance–enhanced asymmetry at finite temperature, with out-of-equilibrium initial conditions (Garbrecht, 2012).

6. Phenomenological and Cosmological Implications

Nonthermal leptogenesis models lead to several significant implications beyond baryogenesis itself:

• Testable Phases and Scales: Phase transitions at scales $\gtrsim 10^9$ GeV, or TeV-scale transitions with novel Higgs sectors or vectorlike fermions, may leave signatures in collider signals, flavor physics, or gravitational wave backgrounds (Ai et al., 10 Oct 2025, Cataldi et al., 23 Jul 2024).
• Primordial Non-Gaussianity: In curvaton/majoron–motivated scenarios, the amplitude of local–type $f_{NL}$ measures the efficiency and timing of nonthermal RHN production and decay, linking leptogenesis with future CMB and large-scale structure observations (Fong et al., 2023).
• Suppression of Washout Problems: The separation of production and washout channels yields "maximal efficiency," making it possible to successfully realize leptogenesis at lower CP asymmetries or smaller RHN masses than traditionally required, and addressing the gravitino problem in supersymmetric models (Huang et al., 2023).
• Baryon–Dark Matter–Dark Energy Unification: SU(2)$_Z$-based models link all three cosmic sectors into a single nonthermal dynamical framework (0810.3341).
• Gravitational Waves: Strongly first-order phase transitions and cosmic strings formed during $U(1)_{B-L}$ breaking lead to stochastic GW backgrounds within reach of future interferometers (Huang et al., 2022, Cataldi et al., 23 Jul 2024).
• Lepton Flavor Violation and EDMs: Soft parameters required for nonthermal $CP$ violation in supersymmetric models are close to present bounds from experiments such as MEG, offering direct experimental prospects (Adhikari et al., 2015).

7. Comparison to Thermal Leptogenesis and Extensions

The nonthermal leptogenesis paradigm removes key thermal constraints:

• No requirement for $T_R > M_N$: Ultraheavy masses for RHNs ($M_N \gtrsim 10^{14}$ GeV) become viable even if reheat or transition temperature is far lower (Cataldi et al., 23 Jul 2024), enabling high- or GUT-scale leptogenesis without overclosure or excessive washout.
• Wash-In Mechanisms: Reprocessing of primordial conserved charges into a $B-L$ asymmetry via strong LNV interactions even when there is no decay CP violation, as in "wash-in leptogenesis" (Domcke et al., 2020).
• Inclusion of Dirac and Exotic Neutrino Sectors: Lepton-number–violating interactions even with Dirac neutrinos extend the standard mechanism (Heeck, 2013).

A salient feature is the flexibility in handling cosmological and experimental constraints—notably, relaxation of the Davidson–Ibarra bound, minimized requirement on the CP-violating phase, and compatibility with low reheat temperatures or otherwise problematic thermal histories.

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In summary, nonthermal leptogenesis encompasses a suite of mechanisms for baryogenesis in the early Universe where the key lepton-number–violating species are produced by non-equilibrium processes outside the standard thermal plasma. These mechanisms exploit diverse features of cosmological evolution—such as inflation, phase transitions, topological defects, or dynamically varying couplings—to generate the lepton asymmetry in ways that suppress washout and permit connections to a broad swath of phenomena in particle physics, cosmology, and experimental probes.