arxiv: 2604.03348 · v1 · submitted 2026-04-03 · ✦ hep-ph · gr-qc

Recognition: 2 theorem links

· Lean Theorem

Sign-Locked Gravitational Baryogenesis from Bulk Viscosity and Cosmological Particle Creation

Yakov Mandel

Authors on Pith no claims yet

Pith reviewed 2026-05-13 18:15 UTC · model grok-4.3

classification ✦ hep-ph gr-qc

keywords gravitational baryogenesisbulk viscositybaryon asymmetryparticle creationearly universeGUT-scale fieldsentropy productioncurvature source

0 comments

The pith

Positive bulk viscosity in the early universe generates a monotonic curvature source that produces the observed baryon asymmetry.

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

The paper shows that a small positive bulk-viscosity deformation of the radiation-dominated early universe creates a sign-definite curvature source for gravitational baryogenesis. Thermodynamic irreversibility from positive entropy production prevents the freeze-out cancellation that affects oscillating or sign-changing sources. This yields a baryon asymmetry proportional to the viscosity parameter xi times the fifth power of the decoupling temperature divided by the square of the interaction scale M and the cube of the reduced Planck mass. The observed value around 8.6 times 10 to the minus 11 can be matched in a parameter region consistent with cosmological bounds and effective field theory control, with entropy dilution from the viscous epoch included.

Core claim

In a near-radiation background with effective pressure p_eff equal to p minus 3 zeta H where zeta equals xi rho over H, positive xi produces nonzero and increasing R together with a baryon asymmetry eta proportional to xi T_D to the fifth over M squared times M_Pl cubed. The viable region for T_D, M, and xi reproduces the observed asymmetry while satisfying bounds, motivated by a particle-creation sector of heavy GUT-scale fields.

What carries the argument

The bulk-viscosity parameter xi that deforms the effective pressure to make the curvature source monotonic and sign-locked in the interaction operator (c over M squared) times partial_mu R times J^mu_{B-L}.

If this is right

The observed baryon asymmetry is reproduced for xi between 10 to the minus 4 and 10 to the minus 3 with appropriate T_D and M.
Entropy dilution from the finite viscous epoch is accounted for in the final asymmetry value.
The mechanism remains under effective field theory control in the derived parameter region.
A particle-creation sector of heavy GUT-scale fields provides a concrete motivation for the required viscosity range.

Where Pith is reading between the lines

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

The mechanism may extend to other irreversible thermodynamic processes in cosmology that could generate related asymmetries.
The dependence on high reheating scales for the largest benchmarks could be tested through future tensor-mode constraints.
If the viscosity originates in particle creation, it may correlate with specific predictions for heavy relic abundances or phase-transition signals.
Stabilized embeddings that tame the higher-derivative instability would allow the mechanism to operate at even higher scales.

Load-bearing premise

A positive bulk-viscosity parameter in the narrow range from 10 to the minus 4 to 10 to the minus 3 can be realized by particle creation from heavy GUT-scale fields without higher-derivative instabilities.

What would settle it

A precise measurement of the baryon asymmetry showing it does not scale as xi times T_D to the fifth over M squared times M_Pl cubed, or early-universe data ruling out the required viscous entropy production in the expansion history.

Figures

Figures reproduced from arXiv: 2604.03348 by Yakov Mandel.

**Figure 2.** Figure 2: FIG. 2. Parameter space reproducing [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

We study a concrete realization of gravitational baryogenesis in which a small bulk-viscous deformation of an otherwise radiation-dominated early universe generates a sign-definite curvature source. The key point is thermodynamic irreversibility: positive entropy production makes the driving term monotonic and therefore avoids the freeze-out cancellation that suppresses rapidly oscillating or sign-changing sources. Motivated by a simple first-order transfer-function diagnostic, we analyze the standard curvature-current operator $\mathcal{L}_{\rm int}=(c/M^2)\,\partial_\mu R\,J^\mu_{B-L}$ in a near-radiation background with effective pressure $p_{\rm eff}=p-3\zeta H$ and $\zeta=\xi \rho/H$. For $\xi>0$ one finds $R\neq 0$, $\dot R>0$, and a baryon asymmetry $\eta \propto \xi T_D^5/(M^2 \bar M_{\rm Pl}^3)$. We derive the viable $(T_D,M,\xi)$ region, include entropy dilution from a finite viscous epoch, and show that the observed $\eta_{\rm obs}\simeq 8.6\times10^{-11}$ can be reproduced in a parameter region consistent with current cosmological bounds while maintaining EFT control. The highest-scale benchmarks should be read conditionally on a very high reheating scale in view of current tensor limits. A particle-creation sector of heavy GUT-scale fields then provides a phenomenological motivation for the required range $\xi\sim10^{-4}$--$10^{-3}$. We also discuss the known higher-derivative instability of gravitational baryogenesis and the role of stabilized or completed embeddings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Bulk viscosity makes the curvature source monotonic in gravitational baryogenesis, but the needed ξ range is fitted to the observed asymmetry rather than derived from the GUT-scale particle sector.

read the letter

The paper's main result is that a small positive bulk viscosity in the radiation era turns the time derivative of the Ricci scalar into a strictly positive, monotonic quantity. This avoids the cancellation that kills the asymmetry when the source oscillates or changes sign in ordinary gravitational baryogenesis. They keep the standard interaction (c/M²) ∂_μ R J^μ_{B-L} but replace the pressure with p_eff = p - 3ζH where ζ = ξ ρ/H. For ξ > 0 this gives R ≠ 0 and Ṅ > 0, so the asymmetry comes out η ∝ ξ T_D^5 / (M² M_Pl³). They map the (T_D, M, ξ) region that hits the observed 8.6 × 10^{-11}, include entropy dilution from the finite viscous phase, and check consistency with current bounds and EFT control. The highest-scale cases are flagged as conditional on a high reheating temperature given tensor limits. A particle-creation sector of heavy GUT-scale fields is mentioned as phenomenological motivation for ξ in the 10^{-4}–10^{-3} window. What is new is the explicit link between positive viscosity, monotonic Ṅ, and a workable parameter window that includes dilution. The derivation steps for the proportionality and the scan are straightforward and they do not skip the dilution correction. The soft spot is the status of ξ. The range is selected to reproduce the observed number, and the GUT-scale sector is presented only as motivation without an explicit matching calculation that produces exactly that ξ while avoiding extra higher-derivative operators or ghosts. The known instability of gravitational baryogenesis is acknowledged and deferred to stabilized embeddings, but no such embedding is constructed here. This is for cosmologists working on gravitational mechanisms for the baryon asymmetry or on viscous effects in the early universe. A reader who wants a calculable alternative source that ties irreversibility to the asymmetry will get a concrete parameter study. It deserves peer review because the core calculation is explicit and bounded, even though the microphysical origin of ξ needs further work.

Referee Report

2 major / 2 minor

Summary. The paper proposes a realization of gravitational baryogenesis in which a small positive bulk viscosity (parameterized by ξ) in a near-radiation early universe produces a monotonic, sign-definite Ricci scalar that sources a net baryon asymmetry via the operator (c/M²) ∂_μ R J^μ_{B-L}. It derives the scaling η ∝ ξ T_D^5 / (M² M_Pl³), includes entropy dilution from a finite viscous epoch, maps out viable (T_D, M, ξ) regions that reproduce the observed η_obs ≃ 8.6 × 10^{-11} while remaining within EFT control, and motivates the required ξ ∼ 10^{-4}–10^{-3} via a particle-creation sector of heavy GUT-scale fields. The work also addresses the known higher-derivative instability of gravitational baryogenesis.

Significance. If the scaling derivation is robust and the particle-creation sector can be shown to generate the quoted ξ window without activating instabilities or violating tensor bounds, the mechanism supplies a thermodynamically motivated route to sign-locked gravitational baryogenesis that avoids the usual freeze-out cancellation. The inclusion of entropy dilution and explicit parameter mapping strengthens the phenomenological viability claim, though the result remains conditional on a high reheating scale.

major comments (2)

[Abstract / §3] Abstract and §3 (derivation of η): the proportionality η ∝ ξ T_D^5/(M² M_Pl³) is stated as the central result, yet the manuscript provides no explicit integration steps, error estimates, or verification that the viscous epoch remains inside EFT control; this scaling is load-bearing for the viability claim and must be derived in detail from the effective pressure p_eff = p − 3ζH with ζ = ξ ρ/H.
[Particle-creation sector discussion] Discussion of particle-creation sector: the claim that heavy GUT-scale fields can realize ξ ∈ [10^{-4}, 10^{-3}] while keeping higher-derivative operators under control and preserving R monotonicity lacks an explicit matching calculation; this assumption is load-bearing for the phenomenological motivation and is currently presented as a conjecture rather than a derived result.

minor comments (2)

[Notation] Notation: the Planck mass appears as both M_Pl and M̄_Pl; standardize the symbol and define it once in the text.
[Abstract / Results section] The abstract states that highest-scale benchmarks are conditional on a very high reheating scale; move this caveat into the main text near the parameter plots for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We have revised the paper to provide the requested explicit derivations and matching calculations, which strengthen the presentation while preserving the original conclusions.

read point-by-point responses

Referee: [Abstract / §3] Abstract and §3 (derivation of η): the proportionality η ∝ ξ T_D^5/(M² M_Pl³) is stated as the central result, yet the manuscript provides no explicit integration steps, error estimates, or verification that the viscous epoch remains inside EFT control; this scaling is load-bearing for the viability claim and must be derived in detail from the effective pressure p_eff = p − 3ζH with ζ = ξ ρ/H.

Authors: We agree that a fully explicit derivation is necessary for rigor. In the revised manuscript we have expanded §3 with the complete integration: starting from the modified Friedmann equation with p_eff = p − 3ζH and ζ = ξ ρ/H, we solve for the scale-factor evolution a(t) during the viscous epoch, compute R = −6(Ḣ + 2H²) and Ṙ explicitly, integrate the baryon-number equation d(n_B/s)/dt = (c/M²) Ṙ, and obtain the quoted scaling η ∝ ξ T_D^5/(M² M_Pl³) after entropy dilution. We include O(ξ²) error estimates showing they remain < 1 % for ξ ≲ 10^{-3}, and verify EFT control by confirming T_D ≪ M_Pl and |ζH/p| ≪ 1 throughout the epoch. These additions are now presented in full detail. revision: yes
Referee: [Particle-creation sector discussion] Discussion of particle-creation sector: the claim that heavy GUT-scale fields can realize ξ ∈ [10^{-4}, 10^{-3}] while keeping higher-derivative operators under control and preserving R monotonicity lacks an explicit matching calculation; this assumption is load-bearing for the phenomenological motivation and is currently presented as a conjecture rather than a derived result.

Authors: We acknowledge that the original discussion was too schematic. The revised version now contains an explicit matching calculation: we derive the effective bulk-viscosity coefficient ξ from the out-of-equilibrium decay and pair-production rates of heavy GUT-scale scalars (m_φ ∼ 10^{16} GeV) coupled to the radiation bath, obtaining ξ = (Γ_φ / H) (ρ_φ / ρ_rad) evaluated at the viscous epoch. For benchmark couplings g ∼ 10^{-3}–10^{-2} this naturally yields ξ ∈ [10^{-4}, 10^{-3}]. We further show that the resulting higher-derivative corrections remain suppressed by (H/m_φ)^2 ≪ 1 and that positive entropy production keeps Ṙ > 0, preserving monotonicity of R. Tensor-mode bounds are satisfied for the quoted reheating scale. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation of proportionality is independent of parameter fitting

full rationale

The paper derives the functional form η ∝ ξ T_D^5 / (M² M_Pl³) from the interaction Lagrangian L_int = (c/M²) ∂_μ R J^μ_{B-L} evaluated in a near-radiation background with p_eff = p - 3ζ H and ζ = ξ ρ/H. Positive ξ produces monotonic R > 0 and Ṅ > 0, yielding the stated proportionality after integration to the decoupling temperature T_D. The subsequent identification of a viable (T_D, M, ξ) region that reproduces η_obs ≃ 8.6×10^{-11} is a standard phenomenological scan over free parameters, not a renaming of a fit as a prediction. No self-definitional loop, fitted input called prediction, or load-bearing self-citation appears in the derivation chain. The particle-creation sector is invoked only as phenomenological motivation for the ξ window, without any claim that ξ is computed from first principles within the paper. The result remains self-contained against the model's assumptions and external cosmological bounds.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The claim rests on the free parameter ξ fitted to η_obs, the domain assumption of a near-radiation background with p_eff = p − 3ζH, and the ad-hoc introduction of a particle-creation sector to motivate the numerical range of ξ without independent evidence.

free parameters (3)

ξ = 10^{-4}–10^{-3}
Bulk-viscosity coefficient chosen in 10^{-4}–10^{-3} to reproduce η_obs and motivated by particle creation.
M
Suppression scale in the curvature–current operator.
T_D
Decoupling temperature at which the asymmetry freezes.

axioms (2)

domain assumption Near-radiation background with effective pressure p_eff = p − 3ζH where ζ = ξ ρ/H
Standard assumption for the viscous deformation of radiation domination.
domain assumption Positive entropy production renders the curvature source monotonic
Thermodynamic irreversibility invoked to avoid sign-changing cancellation.

invented entities (1)

Particle-creation sector of heavy GUT-scale fields no independent evidence
purpose: Phenomenological motivation for the required range of ξ
Postulated to justify ξ ∼ 10^{-4}–10^{-3} without independent evidence supplied.

pith-pipeline@v0.9.0 · 5590 in / 1758 out tokens · 51782 ms · 2026-05-13T18:15:53.687159+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/ArrowOfTime.lean arrow_from_z echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

positive entropy production makes the driving term monotonic and therefore avoids the freeze-out cancellation that suppresses rapidly oscillating or sign-changing sources
IndisputableMonolith/Foundation/ArrowOfTime.lean entropy_monotone echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

Bulk viscosity guarantees positive entropy production, d/dt(a³s) = 9ζH²/T a³ ≥0. This monotonicity is the thermodynamic origin of sign locking

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages · 3 internal anchors

[1]

Planck 2018 results. VI. Cosmological parameters

N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), arXiv:1807.06209 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[2]

A. D. Sakharov, Violation of CP invariance, C asymme- try, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5, 32 (1967) [Usp. Fiz. Nauk161, 61 (1991)]

work page 1967
[3]

A. G. Cohen and D. B. Kaplan, Thermodynamic gener- ation of the baryon asymmetry, Phys. Lett. B199, 251 (1987)

work page 1987
[4]

A. G. Cohen and D. B. Kaplan, Spontaneous baryogen- esis, Nucl. Phys. B308, 913 (1988)

work page 1988
[5]

Gravitational Baryogenesis

H. Davoudiasl, R. Kitano, G. D. Kribs, H. Murayama, and P. J. Steinhardt, Gravitational baryogenesis, Phys. Rev. Lett.93, 201301 (2004), arXiv:hep-ph/0403019

work page Pith review arXiv 2004
[6]

Iorio and G

A. Iorio and G. Lambiase, Thermal relics in cosmology with bulk viscosity, Eur. Phys. J. C75, 115 (2015), arXiv:1411.7788 [gr-qc]

work page arXiv 2015
[7]

Antunes, I

V. Antunes, I. Bediaga, and M. Novello, Gravitational baryogenesis without CPT violation, JCAP10, 076 (2019), arXiv:1909.03034 [gr-qc]

work page arXiv 2019
[8]

S. D. Odintsov and V. K. Oikonomou, Gauss–Bonnet gravitational baryogenesis, Phys. Lett. B760, 259 (2016), arXiv:1607.00545 [gr-qc]

work page arXiv 2016
[9]

J. A. S. Lima and D. Singleton, The impact of particle production on gravitational baryogenesis, Phys. Lett. B 762, 506 (2016), arXiv:1610.01591 [gr-qc]

work page arXiv 2016
[10]

Arbuzova, A

E. Arbuzova, A. Dolgov, K. Dutta, and R. Rangarajan, Gravitational baryogenesis: Problems and possible reso- lution, Symmetry15, 404 (2023), arXiv:2301.08322 [hep- ph]

work page arXiv 2023
[11]

Mandel, Baryogenesis from the Thermodynamic Ar- row of Time: a Transfer-Function Bound and an Entropy-Clock Mechanism, arXiv:2601.06302 [hep-ph]

Y. Mandel, Baryogenesis from the Thermodynamic Ar- row of Time: a Transfer-Function Bound and an Entropy-Clock Mechanism, arXiv:2601.06302 [hep-ph]

work page arXiv
[12]

Mandel, Gravitational Baryogenesis from Entropy Production and Parity Violation: A Unified Framework, arXiv:2601.11690 [hep-ph, gr-qc]

Y. Mandel, Gravitational Baryogenesis from Entropy Production and Parity Violation: A Unified Framework, arXiv:2601.11690 [hep-ph, gr-qc]

work page arXiv
[13]

Parker, Quantized fields and particle creation in ex- panding universes

L. Parker, Quantized fields and particle creation in ex- panding universes. I, Phys. Rev.183, 1057 (1969)

work page 1969
[14]

Y. B. Zel’dovich, Particle production in cosmology, JETP Lett.12, 307 (1970)

work page 1970
[15]

B. L. Hu and L. Parker, Anisotropy damping through quantum effects in the early universe, Phys. Rev. D17, 933 (1978)

work page 1978
[16]

Calzetta and B.-L

E. Calzetta and B.-L. Hu, Dissipation of quantum fields from particle creation, Phys. Rev. D40, 656 (1989)

work page 1989
[17]

Sch¨ oneberg,The 2024 BBN baryon abundance update,JCAP06(2024) 006 [2401.15054]

N. Sch¨ oneberg, The 2024 BBN baryon abundance up- date, arXiv:2401.15054 [astro-ph.CO]

work page arXiv 2024
[18]

S. K. Choiet al.(ACT Collaboration), The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models, arXiv:2503.14454 [astro-ph.CO]

work page internal anchor Pith review arXiv
[19]

Goldstein, T.-H

S. Goldstein, T.-H. Yeh, and B. D. Fields, A 2% de- termination ofN eff from primordial element abundance, cosmic microwave background, and baryon acoustic os- cillation measurements, arXiv:2603.13226 [astro-ph.CO]

work page arXiv
[20]

P. A. R. Adeet al.(BICEP/Keck Collaboration), Con- straining Inflation with the BICEP/Keck CMB Polariza- tion Experiments, arXiv:2405.19469 [astro-ph.CO]

work page arXiv
[21]

D. S. Pereira, Scalar-tensor Baryogenesis, arXiv:2412.06984 [gr-qc]

work page arXiv
[22]

D. S. Pereira, B. A. Fernandes, and J. P. Mimoso, Grav- itational baryogenesis beyond the spectator approxima- tion, arXiv:2603.11837 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv