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REVIEW 2 major objections 4 minor 119 references

Leptogenesis can still produce the observed baryon asymmetry when the Universe reheats below the electroweak scale.

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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T0 review · grok-4.5

2026-07-13 04:09 UTC pith:AT7BBABG

load-bearing objection Useful, carefully executed extension of non-thermal leptogenesis below the sphaleron freeze-out temperature, with consistent Boltzmann and GW calculations under the stated assumptions; the main soft spot is the unquantified preheating regime they themselves flag. the 2 major comments →

arxiv 2607.09282 v1 pith:AT7BBABG submitted 2026-07-10 hep-ph astro-ph.CO

Leptogenesis with sub-electroweak-scale reheating temperature

Basabendu Barman , Arindam Basu , Debasish Borah , Nayan Das This is my paper
classification hep-ph astro-ph.CO
keywords leptogenesisreheatingsphaleronsright-handed neutrinosprimordial gravitational wavesmonomial inflationbaryon asymmetry
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 thermal leptogenesis usually demands a reheating temperature high enough that right-handed neutrinos are produced and electroweak sphalerons stay active. This paper shows that the same observed baryon asymmetry can still be generated even when the final reheating temperature lies below the sphaleron freeze-out temperature of roughly 131 GeV. During the prolonged post-inflationary reheating phase the thermal bath briefly reaches temperatures far above the eventual reheating temperature, so sphalerons remain efficient over a finite window before freezing out near the usual electroweak scale. The authors map the viable parameter space for three concrete reheating channels of a monomial inflaton and show that the same history imprints a characteristic tilt on the primordial gravitational-wave spectrum that future detectors could see.

Core claim

Successful leptogenesis that reproduces the observed baryon asymmetry is possible for reheating temperatures below the sphaleron freeze-out temperature in three perturbative reheating scenarios of a monomial inflaton, because the bath reaches a maximum temperature much higher than the final reheating temperature and sphalerons remain efficient over a finite interval before freezing out near the standard electroweak temperature.

What carries the argument

The time-dependent sphaleron-to-Hubble ratio during reheating: because the Hubble rate is larger than in radiation domination while the bath temperature still climbs to T_max ≫ T_rh, sphalerons stay in equilibrium over a calculable window a_sph ≲ a ≲ a_rh that converts the lepton asymmetry generated by right-handed-neutrino decays into baryon number.

Load-bearing premise

The whole calculation assumes that two-body perturbative decays fully describe reheating even when the inflaton–neutrino coupling is large enough that non-perturbative particle production and inflaton fragmentation should set in.

What would settle it

A future primordial-gravitational-wave measurement that rules out the blue-tilted spectrum predicted for n = 6 (or the intermediate red-tilt of the exclusive right-handed-neutrino reheating channel) at the reheating temperatures required by the baryon-asymmetry contours would exclude the corresponding regions of the model.

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

If this is right

  • The lower bound on the reheating temperature needed for successful leptogenesis can be pushed all the way down to the MeV-scale BBN floor for suitable right-handed-neutrino masses and inflaton couplings.
  • Future gravitational-wave observatories (LISA, DECIGO, CE, ET, BBO) can probe the same parameter space that yields the observed baryon asymmetry through the blue-tilted or red-tilted inflationary spectrum imprinted by the non-standard reheating equation of state.
  • The two distinct reheating channels (direct inflaton decay versus exclusive decay into long-lived right-handed neutrinos) produce qualitatively different gravitational-wave spectral shapes, offering a potential observational discriminator.
  • Flavour effects and preheating dynamics, both omitted here, will further restrict or enlarge the viable windows once included.

Where Pith is reading between the lines

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

  • If preheating for n ≥ 3 really drives the equation of state toward radiation, the viable windows found for large inflaton–neutrino couplings in Scenario B will shrink or disappear, making the low-reheating claim more robust only for the milder couplings of Scenario A.
  • The same temporary high-temperature window that keeps sphalerons active could also open new production channels for dark matter or other relics whose freeze-out temperatures lie between T_rh and T_max.
  • A non-detection of the predicted high-frequency blue tilt by next-generation interferometers would force either higher reheating temperatures or a return to purely thermal leptogenesis.

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 studies leptogenesis during post-inflationary reheating for reheating temperatures below the sphaleron freeze-out temperature T_fo ≃ 131 GeV. Working with a monomial inflaton potential V(ϕ) ∝ ϕ^n, it analyzes three perturbative channels: inflaton decay into SM-like bosons, into SM-like fermions, and exclusively into heavy right-handed neutrinos (with a long-lived N3 completing reheating). Coupled Boltzmann equations for energy densities, RHN number density and B−L asymmetry are solved while tracking the lattice sphaleron rate Γ_sph/H through the non-standard expansion history. The authors show that the thermal bath reaches T_max ≫ T_rh, so sphalerons remain efficient over a finite window a_sph ≲ a ≲ a_rh and convert a lepton asymmetry into the observed Y_B ≃ 8.75×10^{-11}. Viable contours in the (T_rh, y_ϕN) plane are mapped for n = 2, 4, 6 and several RHN masses, and the imprint of the modified expansion history on the primordial gravitational-wave spectrum is computed for future detectors.

Significance. If the results hold under the stated assumptions, the work opens a previously under-explored window for thermal/non-thermal leptogenesis at T_rh as low as a few MeV–100 GeV, well below the electroweak scale. The explicit tracking of Γ_sph during reheating (Sec. 3), the analytic T_max and n_N1(a_rh) scalings, and the concrete GW spectral shapes for both direct and RHN-mediated reheating constitute falsifiable predictions that can be tested by future interferometers. The Scenario-B construction (exclusive inflaton→RHN decay followed by N3-dominated reheating) is a clean, economical extension of earlier non-thermal leptogenesis literature and yields a distinctive red-tilted GW feature. These elements make the paper a useful reference for both particle-physics model building and early-universe cosmology.

major comments (2)
  1. [Sec. 6, Figs. 14–15] Sec. 6 and Figs. 14–15: the viable parameter space for Scenario-B (and the high-y_ϕN branches of Scenario-A with n = 4, 6) relies on y_ϕN ∼ 0.1–0.2. The paper itself notes that such couplings trigger non-perturbative preheating and inflaton fragmentation that drive the equation of state toward w → 1/3, an effect omitted from the Boltzmann system (2.10)–(2.13) and (4.1). Because the central claim that successful leptogenesis is possible for T_rh < T_fo rests on the contours obtained under a purely perturbative description, the authors should either (i) restrict the published contours to the regime where the perturbative approximation is self-consistent (n = 2 and the lower-y_ϕN branches) or (ii) provide a quantitative estimate of how fragmentation alters T(a), Γ_sph/H and the final Y_B.
  2. [Sec. 4, Eqs. (4.1), (4.4)] Eq. (4.1) and the conversion formula (4.4): the analysis assumes that the full 28/79 conversion factor applies throughout the interval a_sph ≲ a ≲ a_rh. For T_rh ≲ 100 GeV the sphaleron freeze-out temperature remains near the standard electroweak value (as the authors correctly note), yet the temperature evolution is non-monotonic and the radiation bath is only partially thermalized. A short numerical check that the integrated sphaleron conversion still yields a factor close to 28/79 (or an explicit statement of the residual uncertainty) would strengthen the claim that the observed Y_B is robustly reproduced.
minor comments (4)
  1. [Fig. 1] Fig. 1 caption and surrounding text: the distinction between bosonic and fermionic T_max scalings is clear, but the gray BBN band is drawn only for T_rh; adding a horizontal line at T_fo would help the reader immediately see the sub-electroweak window under study.
  2. [Sec. 2.2] Eq. (2.17) and the subsequent discussion of a⋆: for n = 2 the kinematic threshold never closes, yet several figures still mark a⋆. A brief clarifying sentence would avoid confusion.
  3. [Note added / Introduction] The concurrent work arXiv:2607.08663 is acknowledged in the Note added; a short comparative paragraph in the introduction or conclusions (rather than only at the end) would better situate the present results for the reader.
  4. [Throughout] Typos: “sphaelron” (p. 2), “asph” vs. a_sph notation inconsistency in Figs. 8–9, and occasional missing spaces around “T_rh”.

Circularity Check

0 steps flagged

No circularity: free parameters (y_φN, y_ν3) are scanned to match observed Y_B; sphaleron rate, CI parametrization, and conversion factor are external inputs; Boltzmann and reheating equations do not reduce the target asymmetry to a quantity defined by that asymmetry.

full rationale

The derivation chain is self-contained against external benchmarks. The CP asymmetry (Eq. 2.5), Casas–Ibarra Yukawas (Eq. 2.2), lattice sphaleron rate (Eq. 3.1 from Ref. [34]), and conversion Y_B ≈ (28/79) Y_{B-L} (Eq. 4.4) are standard external formulae. Reheating energy densities follow from the monomial potential and the continuity equations (2.10), (2.13); the Boltzmann system (4.1) is solved numerically with free parameters {M_1, T_rh, y_φN} (Scenario-A) or {M_1,2, M_3, y_φN, y_ν3} (Scenario-B). Contours in Figs. 14–15 simply mark the loci where the integrated yield equals the observed 8.75 imes10^{-11}; this is ordinary parameter-space exploration, not a prediction forced by construction or by a self-citation uniqueness theorem. The GW spectra (Eqs. 5.7–5.14) are the standard transfer-function result for a given background EoS and are presented as prospective probes, not as circular confirmations of the asymmetry. Self-citations appear only for related prior work on reheating/leptogenesis and are not load-bearing for the central claim. The paper itself flags the perturbative-decay assumption as a limitation (Sec. 6), confirming that the analysis does not hide circularity behind unexamined inputs. Score 0 is therefore required.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The central claim rests on standard Type-I seesaw leptogenesis plus a monomial reheating background. Free parameters are the usual seesaw and reheating knobs tuned to Y_B^obs and T_rh. No new particles beyond the conventional RHNs and inflaton are introduced. Domain assumptions (hierarchical RHNs, wash-out of N_{2,3}, lattice sphaleron rate, instantaneous thermalization, purely perturbative decays) are the load-bearing external inputs.

free parameters (6)
  • y_φN (inflaton–RHN Yukawa)
    Adjusted for each (n, T_rh, M_N) so that the final baryon yield equals the observed value; two solutions typically exist because Y_N(y_φN) is non-monotonic.
  • T_rh
    Free input that fixes the inflaton–SM (or N_3–SM) coupling; scanned from BBN floor (~4 MeV) up through and above T_fo.
  • M_1 (lightest RHN mass)
    Scanned over 10^9–10^12 GeV range; sets both the CP asymmetry and the kinematic window for non-thermal production.
  • M_3 and y_ν3 (Scenario-B only)
    Chosen so that N_3 is long-lived enough to dominate and reheat at the desired T_rh while remaining BBN-safe.
  • n (monomial power)
    Discrete choices n=2,4,6 that control the background equation of state and the T(a) scaling.
  • Complex orthogonal matrix R in Casas–Ibarra parametrization
    Controls the size of the CP asymmetry ε_ΔL for fixed light-neutrino data; not scanned exhaustively.
axioms (6)
  • domain assumption Hierarchical RHN spectrum M_1 ≪ M_2,3 and complete wash-out of any N_2,3-generated asymmetry by N_1 interactions
    Stated in Sec. 2.1; reduces the problem to single-flavour N_1 leptogenesis.
  • domain assumption Sphaleron rate density R_sph given by the SM lattice result of D’Onofrio et al. (Eq. 3.1), including the exponential suppression below T_c ≃ 160 GeV
    Imported without re-derivation for non-radiation-dominated expansion; used throughout Sec. 3–4.
  • domain assumption Instantaneous thermalization of inflaton (or RHN) decay products into a radiation bath with temperature T(a)
    Implicit in the radiation energy-density equations (2.13)–(2.24) and the definition of T_max.
  • ad hoc to paper Perturbative two-body decays dominate the entire reheating process; preheating and fragmentation are negligible
    Assumed for all numerical scans; the paper later acknowledges (Sec. 6) that this fails for the large y_φN required when n>2.
  • domain assumption Monomial potential V(φ)=λ φ^n/Λ^{n-4} during the oscillatory phase, with EoS w=(n-2)/(n+2)
    Standard α-attractor / Starobinsky approximation (Appendix A); fixes all redshifting exponents.
  • ad hoc to paper Vanilla (unflavoured) leptogenesis; charged-lepton Yukawa equilibration effects are ignored
    Explicitly deferred to future work in Sec. 6; prior literature shows flavour can change the yield by O(1).

pith-pipeline@v1.1.0-grok45 · 31860 in / 3916 out tokens · 46133 ms · 2026-07-13T04:09:42.352113+00:00 · methodology

0 comments
read the original abstract

We study the generation of the baryon asymmetry of the Universe via leptogenesis during the post-inflationary reheating epoch, considering reheating temperatures below the temperature of sphaleron freeze-out temperature. Within the framework of a monomial inflaton potential during reheating, we analyze three perturbative reheating scenarios in which the inflaton decays into (i) a pair of SM-like bosons, (ii) a pair of SM-like fermions, or (iii) exclusively into a pair of heavy right-handed neutrinos. For each case, we identify the regions of parameter space that successfully reproduce the observed baryon asymmetry consistently tracking the sphaleron interaction rate during reheating, while satisfying existing cosmological constraints. We also highlight the potential of future primordial gravitational wave observations to probe this class of scenarios.

discussion (0)

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