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arxiv: 2605.00606 · v1 · submitted 2026-05-01 · 🌀 gr-qc · hep-ph

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Non-Supersymmetric Baryogenesis from U(1)-Breaking Scalar Dynamics

Surendra Kumar Gour , Malay K. Nandy
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Pith reviewed 2026-05-09 18:58 UTC · model grok-4.3

classification 🌀 gr-qc hep-ph
keywords baryogenesiscomplex scalar fieldU(1) symmetry breakingNoether chargenonlinear dynamicsearly universe cosmologybaryon asymmetry
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The pith

A complex scalar field with U(1)-breaking potentials generates net charge asymmetry through nonlinear dynamics alone.

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

The paper shows that certain self-interaction potentials for a complex scalar field, by explicitly breaking a global U(1) symmetry, introduce nonlinear source terms into the field's evolution equations. These terms produce a nonzero Noether charge density even when the field starts with equal real and imaginary components and zero initial charge. The charge density falls off as t to the minus three-halves at late times, freezing the baryon-to-photon ratio to a constant value. Different choices of potential yield different mass and coupling dependencies, with one class producing an asymmetry that depends only on the coupling strength and remains viable across broad energy scales.

Core claim

We present a non-supersymmetric mechanism for baryogenesis driven by the nonlinear dynamics of a complex scalar field with generalized self-interaction potentials that explicitly break the global U(1) symmetry. Specifically, three representative forms of the interaction potential are considered, which give rise to intricate nonlinear source terms in the evolution of the field components. In all cases, we show that these nonlinear source terms dynamically generate a nonzero Noether charge density from symmetric initial conditions, providing a purely dynamical origin of charge asymmetry. At late times, the charge density scales as t^{-3/2}, leading to a constant baryon-to-photon ratio through

What carries the argument

The nonlinear source terms in the equations of motion for the real and imaginary parts of the complex scalar field, induced by the explicit U(1) breaking in the generalized self-interaction potentials.

If this is right

  • One class of potentials produces a viable asymmetry over a wide range of scalar masses.
  • A second class requires unrealistically small mass scales to work.
  • A third class makes the final asymmetry independent of scalar mass and dependent only on the coupling parameter.
  • The resulting baryon-to-photon ratio can match the observed value if transfer to Standard Model baryons is efficient and washout is small.

Where Pith is reading between the lines

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

  • The mass-independent case could be tested by searching for the specific coupling value in early-universe relics or collider signatures of light scalars.
  • This purely dynamical charge generation might apply to other global symmetries broken by scalar potentials in cosmological settings.

Load-bearing premise

The generated Noether charge transfers efficiently to the Standard Model sector with negligible washout, and the complex scalar field with the chosen potentials existed in the early universe.

What would settle it

An observation or calculation demonstrating that the late-time charge density does not scale as t^{-3/2} or that the final asymmetry depends on scalar mass in all cases would rule out the mechanism.

Figures

Figures reproduced from arXiv: 2605.00606 by Malay K. Nandy, Surendra Kumar Gour.

Figure 1
Figure 1. Figure 1: Temporal evolution of the dimensionless real and imaginary view at source ↗
Figure 2
Figure 2. Figure 2: Temporal evolution of the dimensionless Noether charge d view at source ↗
Figure 3
Figure 3. Figure 3: Logarithmic plots for the dimensionless Noether charge de view at source ↗
Figure 4
Figure 4. Figure 4: Temporal evolution of ˜ηn(τ ) = ρ˜n(τ) n˜γ(τ) (for n = 1, 2), which is related to baryon-to-photon ratio ηn(t) = ρn(t) nγ(t) . The inset shows that ˜ηn(τ ) remains at stable constant values in the long-time limit, τ → ∞. where the dimensionless photon number density is n˜γ(τ ) = τ −3/2 . (26) From Eqs. 17 and 25, the baryon-to-photon ratio turns out to be ηn(t) = ρn(t) nγ(t) = 1 λ 1 n+1 π 7/2 2ζ(3)  2g∗ 4… view at source ↗
Figure 5
Figure 5. Figure 5: Temporal evolution of the dimensionless real and imaginary view at source ↗
Figure 6
Figure 6. Figure 6: Temporal evolution of the dimensionless Noether charge d view at source ↗
Figure 7
Figure 7. Figure 7: Logarithmic plot for the dimensionless Noether charge den view at source ↗
Figure 8
Figure 8. Figure 8: Temporal evolution of ˜η3(τ ) = ρ˜3(τ) n˜γ(τ) , which is related to baryon￾to-photon ratio η3(t) = ρ3(t) nγ(t) . The inset shows that ˜η3(τ ) remains at a stable constant value in the long-time limit, τ → ∞. From Eq. 27, we may write η1(∞) = 1 λ 1 2 π 7/2 2ζ(3)  2g∗ 45 3/4  M MP 1/2 η˜1(∞) (31) η2(∞) = 1 λ 1/3 π 7/2 2ζ(3)  2g∗ 45 3/4  M MP 1/6 η˜2(∞) (32) which, using Eq. 30 translate to η1 = 1.640… view at source ↗
read the original abstract

We present a non-supersymmetric mechanism for baryogenesis driven by the nonlinear dynamics of a complex scalar field with generalized self-interaction potentials that explicitly break the global $U(1)$ symmetry. Specifically, three representative forms of the interaction potential are considered, which give rise to intricate nonlinear source terms in the evolution of the field components. In all cases, we show that these nonlinear source terms dynamically generate a nonzero Noether charge density from symmetric initial conditions, providing a purely dynamical origin of charge asymmetry. At late times, the charge density scales as $\sim t^{-3/2}$, leading to a constant baryon-to-photon ratio through dynamical freeze-in. While the qualitative behavior is robust across models, the quantitative features depend sensitively on the interaction structure. We find that one class of potentials yields a viable parameter space over a wide range of scalar masses, whereas another requires unrealistically suppressed mass scales. A third scenario stands out in that the final asymmetry is independent of the scalar mass and depends only on the coupling parameter, enhancing predictivity and allowing compatibility across a broad range of energy scales. Assuming efficient transfer of the generated asymmetry to the Standard Model sector and negligible washout effects, the mechanism can account for the observed baryon asymmetry.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a non-supersymmetric baryogenesis mechanism driven by the nonlinear dynamics of a complex scalar field whose self-interaction potentials explicitly break a global U(1) symmetry. Three representative potentials are analyzed; each generates a nonzero Noether charge density from symmetric initial conditions via nonlinear source terms in the field equations. The charge density is shown to scale as ∼t^{-3/2} at late times, producing a constant baryon-to-photon ratio through dynamical freeze-in. One potential class yields an asymmetry independent of the scalar mass and dependent only on the coupling. The authors conclude that, assuming efficient transfer of the asymmetry to the Standard Model sector and negligible washout, the mechanism can account for the observed baryon asymmetry.

Significance. If the transfer and washout assumptions hold, the work supplies a purely dynamical, non-supersymmetric route to the baryon asymmetry whose qualitative robustness across potential forms and, in one case, high predictivity (asymmetry fixed by a single coupling) would be noteworthy. The t^{-3/2} scaling that enforces freeze-in is a concrete, potentially testable feature.

major comments (1)
  1. Abstract: The central claim that the mechanism accounts for the observed baryon asymmetry rests on the external assumption of efficient transfer of the scalar Noether charge to Standard Model baryons together with negligible washout. No B/L-violating operators, Boltzmann equations, or transfer simulations are supplied, so the efficiency and washout suppression remain unquantified rather than derived results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the single major comment below and have revised the manuscript to better clarify the scope and assumptions of our work.

read point-by-point responses

  1. Referee: Abstract: The central claim that the mechanism accounts for the observed baryon asymmetry rests on the external assumption of efficient transfer of the scalar Noether charge to Standard Model baryons together with negligible washout. No B/L-violating operators, Boltzmann equations, or transfer simulations are supplied, so the efficiency and washout suppression remain unquantified rather than derived results.

    Authors: We agree that the efficiency of charge transfer to the Standard Model sector and the suppression of washout are assumptions rather than derived results in the present work. The manuscript focuses on the nonlinear scalar dynamics that generate a nonzero Noether charge density from symmetric initial conditions, with the late-time scaling that enables dynamical freeze-in. Explicit B/L-violating operators, Boltzmann equations, or transfer simulations would require a specific UV completion coupling the scalar to SM fields, which is model-dependent and beyond the scope of this paper. We will revise the abstract to state more explicitly that the mechanism supplies a dynamical source of charge asymmetry, and that the observed baryon asymmetry can be obtained assuming efficient transfer and negligible washout in a suitable extension. This separation of asymmetry generation from transfer is standard in many baryogenesis scenarios. revision: yes

Circularity Check

0 steps flagged

Scalar Noether charge generation and late-time scaling derived from EOM; transfer to SM baryons explicitly assumed, not fitted or self-defined

full rationale

The paper derives nonzero Noether charge density from symmetric initial conditions via nonlinear source terms in the scalar field equations of motion for three explicit U(1)-breaking potentials. It then shows the late-time charge density scaling ~t^{-3/2} (yielding constant n/s in radiation domination) directly from the dynamics. The final claim that the mechanism accounts for the observed baryon asymmetry is conditioned on the separate, explicitly stated assumptions of efficient transfer to the SM sector and negligible washout; no equations, operators, or simulations for the transfer are presented as derived results, and no parameters are fitted to the observed asymmetry and then relabeled as predictions. No self-citations, uniqueness theorems, or ansatze imported from prior work appear in the provided text. The derivation chain for the scalar charge is therefore self-contained against external benchmarks and exhibits no reduction to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The claim rests on the existence of the scalar field, the specific form of its U(1)-breaking potentials, and two key transfer assumptions that are not derived from the dynamics.

free parameters (2)
  • scalar mass
    Appears in the quantitative results for two of the three potentials and is stated to be unconstrained in the third.
  • coupling constants in the potentials
    Control the strength of the nonlinear source terms and determine the final asymmetry magnitude.
axioms (2)
  • domain assumption Efficient transfer of the generated Noether charge to Standard Model baryons
    Invoked in the final paragraph to connect the scalar charge to the observed baryon asymmetry.
  • domain assumption Negligible washout effects after charge generation
    Required to preserve the asymmetry until the present epoch.
invented entities (1)
  • Complex scalar field with generalized U(1)-breaking self-interaction potentials no independent evidence
    purpose: To source a net Noether charge through nonlinear dynamics starting from symmetric initial conditions
    The field and its three representative potentials are introduced to realize the mechanism; no independent evidence is provided.

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Reference graph

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