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Quartic inflaton minimum lets leptogenesis survive 4 MeV reheating

2026-07-10 03:22 UTC pith:NZBLBGDB

load-bearing objection Genuine new result on leptogenesis at low reheating temperatures, with two real but addressable limitations. the 2 major comments →

arxiv 2607.08663 v1 pith:NZBLBGDB submitted 2026-07-09 hep-ph astro-ph.CO

Leptogenesis and Low Reheating Temperatures

Marcos A. G. Garcia , Stephen E. Henrich , Wenqi Ke , Keith A. Olive This is my paper
classification hep-ph astro-ph.CO
keywords leptogenesisreheatinginflaton potentialbaryon asymmetryright-handed neutrinoStarobinsky modelkinematic shutofftype-I seesaw
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard leptogenesis — the mechanism that generates the universe's matter-antimatter asymmetry via decays of heavy right-handed neutrinos — is widely thought to fail when the reheating temperature after inflation drops below the electroweak scale of about 130 GeV, because any baryon asymmetry produced earlier gets diluted by entropy release during the long reheating tail. This paper argues that this failure is not intrinsic to leptogenesis itself but is an artifact of assuming the inflaton oscillates in a quadratic potential, where its effective mass stays constant and it continues producing right-handed neutrinos throughout all of reheating. When the inflaton potential has a quartic (or higher) minimum, as arises in generalized Starobinsky-like models, the inflaton's effective mass decreases as the universe expands. The inflaton starts heavy enough to decay into right-handed neutrinos but quickly becomes too light, shutting off that production channel very early. The resulting right-handed neutrino population is fixed at that early moment, decays while sphaleron transitions are still active to convert lepton asymmetry into baryon asymmetry, and then the result simply redshifts to the present. Because the production cutoff happens at a scale factor set by particle masses rather than by the reheating temperature, the final baryon asymmetry becomes essentially independent of the reheating temperature — it can be as low as the 4 MeV bound from big bang nucleosynthesis with no penalty. The asymmetry depends primarily on just two parameters: the coupling between the inflaton and right-handed neutrinos, and the amount of CP violation in neutrino decays.

Core claim

The paper's central result is that for inflaton potentials with a quartic minimum (k=4, giving radiation-like reheating with equation of state w=1/3), the inflaton's decreasing effective mass causes the right-handed neutrino production channel (φ→NN) to shut off kinematically at an early, fixed scale factor a* determined only by the inflaton and neutrino masses. This decouples the final baryon asymmetry from the reheating temperature entirely: the dilution factor that normally kills low-reheating leptogenesis cancels because both the baryon density and the entropy density scale with the reheating temperature in compensating ways. The resulting compact formula (Eq. 5.21) shows Y_B depends on

What carries the argument

The kinematic shutoff mechanism: for k≥4, the inflaton has no vacuum mass, so its effective mass during oscillations is m_eff ∝ ρ_φ^{1/4} ∝ a^{-1}, which starts at ~3×10^13 GeV but drops below 2M_N at a* ≈ 15 a_end. After a*, no more right-handed neutrinos are produced, and the existing population simply redshifts as a^{-3} until it decays. The final asymmetry traces directly to n_N(a*), which is set by the inflaton-neutrino coupling y_{φNN}. The cancellation of T_RH dependence arises because T_max ∝ T_RH^{1/4} and s(a*) ∝ T_max^3, so T_RH/(s(a*)·T*) is constant. The hierarchy a* < a_N < a_sph < a_RH ensures that production, decay, sphaleron processing, and reheating happen in the right顺序.

Load-bearing premise

The clean independence of the baryon asymmetry from the reheating temperature requires that right-handed neutrino production shuts off before the inflaton condensate fragments, which holds only when the neutrino mass is above about 1.6×10^11 GeV. The paper fixes the neutrino mass at 10^12 GeV throughout and does not explore whether the mechanism survives at lower masses where fragmentation would modify the production history before shutoff.

What would settle it

If the inflaton potential near its minimum is quadratic (k=2) rather than quartic, the effective mass stays constant, right-handed neutrino production continues throughout reheating, and the dilution factor (T_RH/T_sph)^5 suppresses the asymmetry by more than 10^10 for GeV-scale reheating — making leptogenesis impossible at low temperatures. The paper's claim is that switching to k≥4 eliminates this suppression, which would be falsified if the kinematic shutoff at a* fails to produce the required n_N(a*) or if the hierarchy a* < a_N < a_sph cannot be maintained for viable parameter choices.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Models of dark matter that require very low reheating temperatures (near the 4 MeV BBN floor) no longer face an automatic incompatibility with standard baryogenesis mechanisms.
  • The reheating temperature is freed as a constraint on leptogenesis model-building for k≥4 potentials, widening the viable parameter space for type-I seesaw models.
  • Inflationary model selection now directly impacts baryogenesis feasibility: the shape of the inflaton potential near its minimum (quadratic vs. quartic) determines whether low-reheating leptogenesis succeeds or fails by orders of magnitude.
  • The result reduces the leptogenesis parameter space to essentially two observables (y_{φNN} and the CP phase δ_eff), which could in principle be correlated with neutrino oscillation parameters in specific seesaw embeddings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If future CMB-S4 or LiteBIRD measurements favor an inflationary spectral tilt consistent with k≥4 Starobinsky-like potentials, the mechanism here would be cosmologically viable by construction, linking the tensor-to-scalar ratio directly to baryogenesis feasibility.
  • The independence of the baryon asymmetry from the RHN decay rate y_N (within bounds) suggests that collider probes of heavy neutrino properties would not directly test this leptogenesis channel, making cosmological observations the primary discriminator.
  • The mechanism may extend to other baryogenesis pathways (e.g., electroweak baryogenesis during reheating) whenever the source of CP violation shuts off before sphaleron decoupling, suggesting a broader principle: early-time production cutoffs can replace reheating temperature as the controlling parameter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. This paper studies non-thermal leptogenesis during non-instantaneous reheating in the canonical type-I seesaw framework. The authors show that for generalized Starobinsky-like potentials with a quartic (or higher) minimum (k >= 4), the inflaton's effective mass decreases during reheating, causing a kinematic shutoff of the phi -> NN channel at an early scale factor a*. This shutoff fixes the RHN population early, and the resulting baryon asymmetry becomes largely independent of the reheating temperature, the RHN mass, and the RHN decay rate. The authors derive an analytic expression for the final asymmetry (Eq. 5.21), confirm it with numerical solutions of the Boltzmann equations, and demonstrate that the observed baryon asymmetry can be obtained for T_RH as low as the BBN bound of ~4 MeV. The k=2 (matter-like reheating) case is shown to fail at low T_RH due to severe dilution. The generalization to bosonic reheating and k >= 6 is also discussed.

Significance. The result that standard leptogenesis can work for arbitrarily low reheating temperatures above the BBN bound is significant and counterintuitive, as low T_RH scenarios are typically considered incompatible with standard baryogenesis mechanisms. The T_RH-independence is a genuine analytic result: it arises from the cancellation between the dilution factor (a*/a_RH)^3 and the entropy density s(a_RH) proportional to T_RH^3, and notably does not depend on fragmentation parameters because RHN production is complete well before fragmentation begins. The analytic approximations are transparent and well-validated by numerical solutions (Figs. 3-8). The identification of the kinematic shutoff mechanism as the key qualitative difference between k=2 and k>=4 reheating is a clean physical insight. The extension to bosonic reheating (Section 7) demonstrates the robustness of the mechanism, though it receives less numerical support.

major comments (2)
  1. The abstract states that the final asymmetry is 'largely insensitive to the RHN mass,' and Eq. (5.21) shows an explicit factor of (m_hat / 2 M_N). The text argues this cancels against epsilon proportional to M_N from the type-I seesaw (Eq. 1.12). However, this cancellation is model-specific: it depends on the specific form of epsilon in Eq. (1.12) and the seesaw relation m_nu_i = y_i^2 v^2 / M_i. The claim of M_N-insensitivity is never numerically verified for M_N != 10^12 GeV. Furthermore, as M_N approaches the lower bound ~1.6 x 10^11 GeV (where a* -> a_beta), the sudden-onset fragmentation approximation becomes less reliable and could modify n_N(a*). The authors should either (a) provide numerical results for at least one or two additional values of M_N to substantiate the insensitivity claim, or (b) more carefully qualify the scope of the claim, noting that it holds within the regime
  2. Footnote 18 acknowledges that without instantaneous thermalization, fermionic reheating with a two-fermion final state requires y_phi_ff >= O(1), corresponding to T_RH ~ 10^17 GeV, which is incompatible with the low T_RH values central to the paper's main claim. The regime T_RH ~ 4 MeV requires y_phi_ff ~ 3 x 10^{-4}, far below this bound. While the authors cite [69] for this constraint, the issue is not discussed in the main text. Since the paper's headline result concerns fermionic reheating at low T_RH, this caveat should be prominently stated in Section 5 rather than relegated to a footnote, and the bosonic reheating case (which avoids this issue) should be discussed as the more robust realization of the mechanism. As written, a reader could miss this important limitation.
minor comments (7)
  1. The paper uses g* = 915/4 (MSSM) throughout for concreteness, but notes that none of the key results rely on supersymmetry. For readers not working in SUSY, it would be helpful to briefly state how the numerical results change if the SM value g* = 106.75 is used instead, particularly for the parameter space in Fig. 7.
  2. In Eq. (5.21), the factor g*(a_RH)^{1/4} appears, and the text notes a 'mild sensitivity' to T_RH through g*. It would be useful to quantify this more explicitly, e.g., by stating the range of variation in Y_B across the T_RH range shown in Fig. 8.
  3. The condition in Eq. (5.32) constrains y_N to a range. It would be helpful to show, perhaps as a shaded region in Fig. 7 or 8, where this condition is satisfied, so the reader can verify that the displayed parameter space is self-consistent.
  4. In Fig. 5, the dashed portion of the M_N n_N curve corresponds to T > M_N where the RHNs are relativistic. Clarifying this in the caption (rather than only in the text) would help.
  5. The paper cites [69] (arXiv:2512.16203) for the thermalization constraint in footnote 18. This appears to be a very recent preprint; the authors should verify that the constraint y_phi_ff >= O(1) applies to their specific setup (Starobinsky-like potential, k=4) and not only to the models studied in [69].
  6. Section 7 provides analytic results for k=6 and k=8 with bosonic reheating but no numerical validation. A brief comment on whether the analytic approximations remain accurate for these cases, or a figure analogous to Fig. 3, would be appropriate.
  7. The notation 'c' in Eqs. (5.8) and surrounding text (described as O(0.01-0.1) near a*) is somewhat ambiguous. It is introduced as a correction factor to the decay rate but its precise definition or origin could be stated more clearly.

Circularity Check

0 steps flagged

No significant circularity; central analytic result is self-contained

full rationale

The paper's central result (Eq. 5.21) is derived from standard Boltzmann equations (3.1) with clearly stated physical assumptions (kinematic shutoff at a*, hierarchy a* < a_N < a_sph < a_RH). The derivation chain is: (1) solve the RHN number density Boltzmann equation for a < a* to get n_N(a*) [Eq. 5.6], which depends on y_φNN, ρ_end, M_P, and M_N/ˆm; (2) dilute n_N ∝ a^{-3} from a* to a_RH; (3) convert to Y_B via sphaleron factor 8/23 and entropy s(a_RH) [Eq. 5.18]; (4) observe that T_RH cancels between the dilution factor (a*/a_RH)^3 and the entropy density s(a_RH) ∝ T_RH^3, yielding T_RH-independence [Eq. 5.21]; (5) observe that ε ∝ M_N from the type-I seesaw [Eq. 1.12] cancels the explicit (ˆm/2M_N) factor, yielding M_N-independence. The parameters y_φNN and |ε| are genuinely free model parameters — the paper does not fit them to the baryon asymmetry and then claim a prediction; instead it identifies the (y_φNN, ε) parameter space consistent with the observed Y_B (Figs. 7–8). Self-citations to [41, 46, 63] (with overlapping authors Garcia, Olive) provide numerical inputs such as fragmentation parameters (ξ_0, b, a_β) and the T_RH–y_φff relation (Eq. 2.11), but these do not enter the final baryon asymmetry formula (Eq. 5.21) at all — the T_RH-independence arises purely from the scaling n_N ∝ a^{-3} combined with s ∝ T_RH^3 at reheating, and RHN production is complete at a* ≈ 15a_end, well before fragmentation at a_β ≈ 90a_end. The self-citations are supporting infrastructure, not load-bearing for the central claim. No step in the derivation reduces to its own inputs by construction. Score 1 reflects the presence of self-citations that, while not load-bearing, provide some of the numerical framework.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 1 invented entities

The model introduces no new particles beyond the standard type-I seesaw (RHNs). The generalized potential is a well-motivated extension of the Starobinsky model. The free parameters (y_φNN, ε, y_φff, M_N, y_N) are all standard in non-thermal leptogenesis. The key innovation is identifying how the k≥4 potential's dynamics enable low-T_RH leptogenesis, not introducing new entities.

free parameters (7)
  • y_φNN
    Inflaton-RHN Yukawa coupling. Free parameter of the model; the paper solves for the range (5×10⁻⁵ to 10⁻²) consistent with the observed baryon asymmetry.
  • |ε| or δ_eff
    CP-violating decay asymmetry parameter. Free parameter constrained by the seesaw relation; the paper determines the required range (10⁻⁹ to 3×10⁻⁴).
  • y_φff
    Inflaton-SM fermion coupling, determines T_RH. Treated as a free parameter scanned over 13 orders of magnitude in T_RH.
  • M_N = 10^12 GeV
    Lightest RHN mass, fixed throughout the numerical analysis. The analytic result shows weak (M_N/m_ν) dependence but this is not numerically verified for other values.
  • y_N
    RHN Yukawa coupling to SM leptons and Higgs. Shown to not affect the final asymmetry given the hierarchy condition Eq. (5.32).
  • m_ν,i = 0.05 eV
    Neutrino mass scale, fixed for concreteness; enters through the seesaw relation for δ_eff.
  • k = 4 (primary), 6, 8 (extensions)
    Power of the inflaton potential near the minimum. k=4 is the primary case studied; k≥4 is required for the mechanism.
axioms (6)
  • domain assumption Type-I seesaw mechanism provides the RHN masses and CP violation
    Standard assumption in leptogenesis literature; the CP asymmetry ε is given by Eq. (1.12) from Refs. [56, 57].
  • domain assumption Sphaleron transitions convert B−L to B with ratio 8/23 (MSSM) or 28/79 (SM)
    Standard electroweak baryogenesis result; used in Eq. (1.7) from Ref. [52]. The choice of MSSM ratio is stated to not affect key results.
  • domain assumption Instantaneous thermalization of inflaton decay products
    Stated in Section 4 and footnote 18; affects the radiation number density and hence the relation between Br and n_N/n_R.
  • domain assumption Fragmentation onset at a_β ≈ 90 a_end with sudden approximation
    Approximation from Ref. [63]; the sudden drop in ξ at a_β is a simplification of the actual gradual fragmentation process.
  • domain assumption Non-thermal RHN production dominates over thermal production
    Verified numerically in Section 5 (Eq. 5.5 shows the non-thermal term is orders of magnitude larger), but assumed in the analytic derivation.
  • standard math BBN lower bound on T_RH of ~4 MeV
    External constraint from Refs. [12]; used as the floor for the parameter space scan.
invented entities (1)
  • Generalized Starobinsky potential V(φ) ∝ (1 - e^(-√(2/3) φ/M_P))^k with k≥4 independent evidence
    purpose: Inflaton potential with quartic or steeper minimum enabling radiation-like reheating and kinematic shutoff
    Derivable from no-scale supergravity (Ref. [46]); inflationary observables (n_s, r) are consistent with Planck data for k=4. The potential is a generalization of the well-tested Starobinsky model (k=2).

pith-pipeline@v1.1.0-glm · 39624 in / 3629 out tokens · 544589 ms · 2026-07-10T03:22:26.422469+00:00 · methodology

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read the original abstract

We study leptogenesis during non-instantaneous reheating in the canonical type-I seesaw framework, with the dominant source of right-handed neutrino (RHN) production being non-thermal from inflaton decays ($\phi \rightarrow NN$). While matter-like reheating ($w_\phi=0$) fails to be compatible with standard leptogenesis for very low reheating temperatures, the situation is strikingly different for generalized Starobinsky potentials approximated by $V(\phi)\propto\phi^k$ with $k\geq4$ about the minimum. In the latter cases, the observed baryon asymmetry can readily be obtained for arbitrarily low reheating temperatures above the BBN bound of $\sim4$ MeV. We study radiation-like reheating ($w_\phi=1/3$, $k=4$) in detail, showing that the evolving effective mass of the inflaton condensate leads to kinematic shutoff of the $\phi\rightarrow NN$ channel, which qualitatively changes the leptogenesis dynamics. We include a detailed treatment of the effects of fragmentation of the inflaton condensate. The final baryon asymmetry depends primarily on only two parameters: the inflaton-RHN coupling, $y_{\phi NN}$, and the CP-violating parameter $|\epsilon|$. Interestingly, the final asymmetry is largely insensitive to the RHN mass, the reheating temperature, and the RHN decay rate. While we focus on fermionic reheating, we show that the general features of these results also hold for bosonic reheating to scalars.

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