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REVIEW 2 major objections 4 minor 28 references

Reheating temperature is set by the seesaw scalar's lifetime, not the inflaton's decay width.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-13 06:23 UTC pith:GKEFS46G

load-bearing objection Clean intermediate-state reheating that moves TRH from the inflaton to the seesaw sector, with analytic scalings that hold under the stated approximations. the 2 major comments →

arxiv 2607.08828 v1 pith:GKEFS46G submitted 2026-07-09 hep-ph astro-ph.COhep-th

Seesaw reheating

Yann Mambrini This is my paper
classification hep-ph astro-ph.COhep-th
keywords seesaw reheatingreheating temperatureinflaton decaylepton-number breakingright-handed neutrinossterile-neutrino dark matterrelativistic time dilationthermal history
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.

This paper argues that the Universe need not reheat directly from the inflaton. Instead, the inflaton can dump its energy into a long-lived intermediate scalar tied to lepton-number breaking; that scalar later decays into right-handed neutrinos and only then builds the thermal bath. Because the scalar is born highly relativistic, time dilation suppresses its decay at first, so the plasma temperature rises only gradually; later the scalar itself becomes non-relativistic, adding a new stage to the thermal history. The net result is that the reheating temperature is controlled by the seesaw-sector parameters rather than by the inflaton. A sympathetic reader cares because the same numbers that set neutrino masses and sterile-neutrino dark matter now also fix when radiation domination begins.

Core claim

In the Seesaw Reheating scenario the inflaton decays into a long-lived intermediate scalar S associated with spontaneous lepton-number breaking; S subsequently decays into right-handed neutrinos that thermalize into the radiation bath. Consequently the reheating temperature scales as the square root of the scalar decay width times the Planck mass, TRH ∝ √(Γ_S M_P) ∝ y_N √(m_S M_P), rather than as the usual √(Γ_ϕ M_P). Two dynamical features fix the history: relativistic time dilation that initially suppresses the scalar decay, and the later relativistic-to-non-relativistic transition of S that introduces a new characteristic timescale.

What carries the argument

The Seesaw Reheating chain ϕ → SS → (N_R N_R)(N_R N_R), governed by the coupled Boltzmann equations that include the effective decay rate Γ_eff_S = Γ_S / γ_S with Lorentz factor γ_S evolving as the characteristic momentum redshifts.

Load-bearing premise

The entire analytic history rests on approximating the whole scalar population by a single characteristic momentum that redshifts as 1/a, together with the claim that the right-handed neutrinos thermalize instantly so their energy can be treated as ordinary radiation.

What would settle it

A full numerical solution of the Boltzmann equations that evolves the complete momentum distribution of S (instead of a single characteristic p_S) and includes finite thermalization rates for the right-handed neutrinos would either recover or quantitatively spoil the claimed scalings for ρ_R and T_RH.

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

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 / 4 minor

Summary. The paper introduces Seesaw Reheating: after inflation the inflaton decays into a long-lived intermediate scalar S associated with spontaneous lepton-number breaking, and the Universe is reheated only when S decays into right-handed neutrinos. Consequently TRH is controlled by the seesaw-sector lifetime rather than by Γ_ϕ. Using the Boltzmann system (5)–(6) and a characteristic-momentum approximation for the Lorentz factor of S, the authors obtain analytic source-dominated scalings for ρ_S and ρ_R through the inflaton-dominated, relativistic-S and non-relativistic-S stages, culminating in the parametric relation TRH ∝ √(Γ_S M_P). When S is identified with the B-L-breaking scalar the same relation links TRH to the type-I seesaw scale and to sterile-neutrino dark matter.

Significance. If the approximations hold, the work cleanly relocates the reheating temperature from the inflaton sector to the seesaw sector and supplies a concrete, analytically tractable thermal history that includes a prolonged low-temperature phase and an extra characteristic timescale set by the relativistic-to-non-relativistic transition of S. The resulting bridge between laboratory neutrino parameters and early-Universe cosmology is a genuine conceptual advance within the standard Boltzmann-reheating framework. The analytic scalings and the benchmark evolution of Fig. 1 are transparent and falsifiable once the deferred companion analyses appear.

major comments (2)
  1. [Analytical Understanding / Eqs. (4)–(5), (13)] The central claim TRH ∝ √(Γ_S M_P) rests on the characteristic-momentum approximation γ_S ∝ a^{-1} that enters Γ_eff_S in Eqs. (4)–(5) and drives every subsequent source-dominated solution (ρ_R ∝ a, then a^{-1}, then a^{-3/2}). Because the full momentum distribution is deferred, the Letter should at least quantify the expected correction to the analytic TRH (or to N_NR) under a realistic spectrum, or demonstrate that the single-p_S result is robust within the hierarchical regime m_S ≪ m_ϕ/2 used throughout.
  2. [The Seesaw Reheating Mechanism / after Eq. (5)] The identification of the right-handed-neutrino energy density with radiation (ρ_R) assumes Γ_th ≫ H for the entire parameter space of interest. The text states that this is verified a posteriori for the benchmark of Fig. 1, yet no explicit estimate or scan is provided. A short analytic or numerical check that Γ_th/H remains large down to the lowest TRH considered would make the radiation-bath identification load-bearing rather than provisional.
minor comments (4)
  1. [Fig. 1] Fig. 1 caption and legend use both y_N and y_S for the same Yukawa; the Lagrangian (1) writes y_N. Unify the notation.
  2. [The Seesaw Reheating Mechanism] The vacuum expression for Γ_S is used while the time-dependent mass induced by the oscillating condensate is deferred. A one-sentence estimate of the kinematic delay for the benchmark point would help the reader judge whether the minimal scenario is already representative.
  3. [Analytical Understanding] Eq. (25) writes TRH ∝ λ_S^{1/4} √(y_N M_P M_N); the subsequent numerical example quotes only M_N and TRH. Adding the corresponding λ_S (or v_S) would make the seesaw connection fully explicit.
  4. [Throughout] A few typographical inconsistencies appear (e.g., “SEESA W”, “REHEA TING” in section headings; “N R” vs. NR). These are easily cleaned.

Circularity Check

0 steps flagged

No significant circularity: TRH scaling and history follow from the stated Lagrangian, Boltzmann system, and characteristic-momentum approximation without reducing to inputs by construction.

full rationale

The paper introduces a minimal Lagrangian (Eq. 1) with the decay chain ϕ→SS→NRNR, writes the vacuum widths (Eq. 3), inserts the time-dilation factor Γ_eff_S=Γ_S/γ_S under the explicit characteristic-momentum approximation p_S∝a^{-1} (Eq. 4), and solves the coupled Boltzmann+Friedmann system (Eqs. 5–6). All subsequent analytic scalings (ρ_S∝a^{-3/2}, ρ_R∝a during inflaton domination; a_NR≃m_ϕ/(2m_S); later ρ_R∝a^{-1} then a^{-3/2}; and the final TRH∝√(Γ_S M_P)) are direct consequences of those equations under the stated approximations. The identification of S with the lepton-number-breaking scalar then yields the parametric link to MN and m_ν by substitution, not by redefinition. Self-citations (e.g., to Garcia–Kaneta–Mambrini–Olive reheating papers) supply only the standard Boltzmann machinery already written out in Eqs. 5–6; they do not force the new intermediate-scalar dynamics or the TRH∝√Γ_S result. No parameters are fitted to data and re-labeled as predictions, no uniqueness theorem is imported, and no known empirical pattern is merely renamed. The two weakest assumptions (characteristic-momentum approximation and prompt NR thermalization) are openly flagged as simplifications deferred to companion papers; they do not render the derivation circular. The Letter is therefore self-contained once its premises are granted.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 1 invented entities

The central claim rests on standard cosmological evolution plus a minimal seesaw-inspired Lagrangian and two technical approximations whose full justification is deferred. Free parameters appear only in the illustrative benchmark; the analytic TRH scaling itself is parameter-free once Γ_S is given. The intermediate scalar is not a wholly new particle but is identified with the existing lepton-number-breaking field of the type-I seesaw.

free parameters (1)
  • benchmark masses and couplings (m_ϕ, m_S, M_N, μ, y_N, ρ_end)
    Chosen by hand to produce the illustrative evolution in Fig. 1; the analytic TRH scaling does not depend on their specific values, only on the hierarchical regime m_S ≪ m_ϕ/2.
axioms (5)
  • domain assumption Post-inflationary Universe described by the Friedmann equation and the three coupled Boltzmann equations for ρ_ϕ, ρ_S, ρ_R with the given decay widths.
    Standard in perturbative reheating literature; invoked from Eq. (5) onward.
  • domain assumption Inflaton oscillates in a quadratic potential and behaves as pressureless matter.
    Stated at the opening of the mechanism section; generalizations to ϕ^k are deferred.
  • ad hoc to paper Characteristic-momentum approximation: a single p_S ∝ a^{-1} determines γ_S for the whole population.
    Explicitly introduced to close the analytic system; full distribution treatment promised elsewhere.
  • domain assumption Right-handed neutrinos thermalize promptly (Γ_th ≫ H) so their energy density can be identified with radiation.
    Stated after Eq. (5); claimed to hold a posteriori for the parameter space shown.
  • ad hoc to paper Vacuum expression for Γ_S is used; time-dependent mass from the oscillating condensate is neglected.
    Author notes the effect can delay the kinematic opening of ϕ→SS and defers a self-consistent treatment.
invented entities (1)
  • Seesaw Reheating chain (ϕ → SS → NRNR with long-lived intermediate scalar) independent evidence
    purpose: To make TRH a probe of the seesaw sector rather than the inflaton and to generate the two characteristic dynamical stages.
    The intermediate scalar is identified with the standard lepton-number-breaking field of the type-I seesaw, so it is not a new particle; the reheating pathway itself is the novel construct.

pith-pipeline@v1.1.0-grok45 · 12369 in / 2938 out tokens · 30742 ms · 2026-07-13T06:23:01.923453+00:00 · methodology

0 comments
read the original abstract

We introduce the Seesaw Reheating scenario, in which the inflaton transfers its energy to a long-lived intermediate scalar associated with the spontaneous breaking of lepton number before the Universe is reheated through its decay into right-handed neutrinos. As a result, the reheating temperature is no longer determined by the inflaton decay width but by the dynamics of the seesaw sector. We derive analytical solutions describing the complete reheating history, revealing two characteristic features of this scenario: the relativistic time dilation of the intermediate scalar, which suppresses its decay and delays the transfer of energy to the thermal bath, and its subsequent transition from a relativistic to a non-relativistic regime, introducing a new characteristic timescale in the thermal history. Together, these effects lead to simple analytical expressions for the reheating temperature. When the intermediate scalar is identified with the field responsible for the spontaneous breaking of lepton number, the same framework naturally connects the reheating temperature to the origin of neutrino masses and provides a well-motivated setting for sterile-neutrino dark matter.

Figures

Figures reproduced from arXiv: 2607.08828 by Yann Mambrini.

Figure 1
Figure 1. Figure 1: Within the characteristic-momentum approxima￾tion introduced above, this transition can be estimated analytically from pS ≃ mS, yielding aNR aend ≃ mϕ 2mS , NNR ≡ ln  aNR aend  ≃ ln mϕ 2mS  , (13) where NNR denotes the epoch at which the intermedi￾ate scalar becomes non-relativistic. In the hierarchical regime mS ≪ mϕ/2 considered here, the scalars are pro￾duced highly relativistically. For the benchma… view at source ↗

discussion (0)

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Reference graph

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