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arxiv: 2605.16212 · v1 · pith:3K4D4KGVnew · submitted 2026-05-15 · ✦ hep-ph · gr-qc

Impact of spectator fields and non-minimal couplings in spontaneous baryogenesis

Mattia Dubbini This is my paper

Pith reviewed 2026-05-20 16:15 UTC · model grok-4.3

classification ✦ hep-ph gr-qc
keywords spontaneous baryogenesisnon-minimal couplingspectator fieldbaryon asymmetryinflaton reheatinggravity couplingbaryon-to-entropy ratio
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The pith

Non-minimal coupling of the inflaton to gravity raises its effective mass and enables spontaneous baryogenesis to generate 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 examines spontaneous baryogenesis with two extensions to the standard setup. A non-minimal gravitational coupling to the inflaton increases its effective mass squared, which favors decays into fermion pairs that violate baryon number during reheating and produces a baryon asymmetry matching cosmological data. A second extension adds a complex scalar spectator field coupled biquadratically to the inflaton and also non-minimally to gravity; this further increases asymmetry production yet still leaves the baryon-to-entropy ratio below observed values. The work shows how gravitational interactions during the reheating epoch can control the final matter-antimatter imbalance without introducing new particles beyond the inflaton and spectator.

Core claim

The non-minimal coupling between gravity and the inflaton increases the effective mass squared of the inflaton, thereby making decays into fermion-antifermion pairs through baryon-number violating processes more likely during reheating. Accordingly, the model yields an overall baryon asymmetry consistent with cosmological observations. When a complex scalar spectator field is added with a biquadratic coupling to the inflaton and its own non-minimal gravitational interaction, the background production is enhanced but the predicted baryon-to-entropy ratio remains smaller than the experimental data.

What carries the argument

Non-minimal coupling of the inflaton to gravity, which modifies the inflaton's effective mass squared and thereby alters the branching ratio of its decays into baryon-number-violating channels during reheating.

If this is right

  • The baryon-to-entropy ratio reaches the range required by cosmological observations when the non-minimal coupling is included.
  • Baryon-number violating processes become the dominant decay channel for the inflaton during reheating.
  • The spectator field further boosts asymmetry production through its biquadratic interaction while its own non-minimal coupling modulates the result.
  • The overall mechanism remains viable even when the inflaton potential is extended by gravitational terms.

Where Pith is reading between the lines

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

  • Similar non-minimal couplings could be applied to other inflaton potentials to adjust asymmetry without changing the reheating temperature.
  • The spectator field might serve as a tunable parameter in related models of leptogenesis or axion-driven baryogenesis.
  • Future precision measurements of the reheating temperature could constrain the size of the non-minimal coupling constant required here.

Load-bearing premise

The non-minimal coupling between gravity and the inflaton increases the effective mass squared of the inflaton enough to make baryon-number violating decays dominant during reheating.

What would settle it

A direct calculation of the inflaton decay rate into fermions without the non-minimal coupling term that shows the baryon asymmetry falls short of the observed value by more than an order of magnitude.

Figures

Figures reproduced from arXiv: 2605.16212 by Mattia Dubbini.

Figure 1
Figure 1. Figure 1: Left: contour plot of the allowed region of the log (g) − log |ξ| plane, compatible with the observational constraint η = (8.59 ± 0.10) × 10−11 . Right: ratio between our η from Eq. (4) and the background’s result as function of ξ, for g = 0.0001 and g = 0.001. 4. Complex scalar spectator field As a second improvement of the background paradigm, we extend the Lagrangian model in Eq. (1) considering the fol… view at source ↗
Figure 2
Figure 2. Figure 2: Top: ratio between η from Eq. (7) and the background’s result as function of ξ and σ, for fixed values g = 0.01, g = 0.001, g = 0.0001, and ϕI = 10−3f. Bottom: contour plot of the allowed region in the log(g) − log(ξ) and log(g) − log(σ) planes, compatible with the observational constraint η = (8.59±0.10)×10−11; gray areas are excluded by the lower bound TRH = 1010 GeV. 3. G. R. Farrar and M. E. Shaposhnik… view at source ↗
read the original abstract

We investigate the model of spontaneous baryogenesis, considering two extensions to the background paradigm. Firstly, we introduce a non-minimal coupling between gravity and the inflaton, increasing the effective mass squared of the latter. In this way, the inflaton decays more likely into fermion-antifermion pairs during reheating, through baryon-number violating processes. Accordingly, we obtain an overall baryon asymmetry consistent with cosmological observations. Then, we consider a complex scalar spectator field interacting with the inflaton through a biquadratic coupling and non-minimally with gravity, and analyze the impact in terms of baryon asymmetry production. In this scenario too, the background model results significantly enhanced, but the predicted baryon-to-entropy ratio remains smaller than the experimental data.

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 / 2 minor

Summary. The manuscript investigates spontaneous baryogenesis in an inflationary setting, extending the standard paradigm with a non-minimal coupling of the inflaton to gravity and the inclusion of a complex scalar spectator field. The non-minimal coupling is argued to increase the effective mass of the inflaton, facilitating baryon-number violating decays during reheating and yielding a baryon asymmetry consistent with observations. The spectator field with biquadratic coupling and non-minimal gravity interaction is shown to enhance the asymmetry production, though the resulting baryon-to-entropy ratio falls short of experimental values.

Significance. If the central calculations hold, this work demonstrates how non-minimal couplings and spectator fields can be used to adjust the baryon asymmetry in spontaneous baryogenesis models to match cosmological data. It highlights the role of reheating dynamics in generating the observed η_B. The analysis of two distinct extensions provides a comparative view of their impacts, though the significance is limited by the need for a self-consistent dynamical treatment.

major comments (1)
  1. [Section discussing non-minimal coupling and reheating dynamics] The non-minimal coupling term (presumably ξ φ² R) is introduced to raise the effective mass squared of the inflaton and thereby enhance the decay rate into B-violating fermion-antifermion pairs. However, the same term enters the inflaton Klein-Gordon equation and the Friedmann equation, altering both the oscillation frequency and Hubble evolution during reheating. Treating R as an external background while using the boosted m_eff² omits the back-reaction on the time-dependent decay window and entropy production. Without an explicit solution of the coupled system, the reported η_B consistent with observations rests on an uncontrolled approximation. This issue is load-bearing for the central claim in the non-minimal coupling scenario.
minor comments (2)
  1. [Abstract] The abstract states that parameters are adjusted to reach observed asymmetry levels but does not provide the explicit numerical value of the resulting baryon-to-entropy ratio or the specific range of the non-minimal coupling strength used.
  2. [Section on spectator field] Clarify the definition and range of the biquadratic coupling constant in the spectator field scenario to make the enhancement of the background model more transparent.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive major comment on the treatment of non-minimal couplings during reheating. We address this point directly below and agree that additional work is needed to strengthen the analysis.

read point-by-point responses

  1. Referee: [Section discussing non-minimal coupling and reheating dynamics] The non-minimal coupling term (presumably ξ φ² R) is introduced to raise the effective mass squared of the inflaton and thereby enhance the decay rate into B-violating fermion-antifermion pairs. However, the same term enters the inflaton Klein-Gordon equation and the Friedmann equation, altering both the oscillation frequency and Hubble evolution during reheating. Treating R as an external background while using the boosted m_eff² omits the back-reaction on the time-dependent decay window and entropy production. Without an explicit solution of the coupled system, the reported η_B consistent with observations rests on an uncontrolled approximation. This issue is load-bearing for the central claim in the non-minimal coupling scenario.

    Authors: We thank the referee for identifying this important consistency issue. In the current manuscript we compute the inflaton decay rate using the effective mass m_eff² = m² + 6ξR (with R taken from the background Friedmann equation) while retaining the standard oscillatory solution for the inflaton amplitude and Hubble evolution. This is indeed an approximation that neglects the back-reaction of the non-minimal term on the Klein-Gordon equation and the resulting changes to the oscillation frequency, the duration of the reheating epoch, and entropy production. We agree that a fully self-consistent numerical or analytic solution of the coupled system would be preferable. In the revised manuscript we will add an explicit estimate of the size of the back-reaction for the parameter values that yield the observed η_B, together with a brief numerical check of the modified equations for representative ξ. This will either confirm the robustness of our results or quantify the uncertainty introduced by the approximation, thereby supporting the central claim more rigorously. revision: yes

Circularity Check

0 steps flagged

Derivation remains self-contained; no load-bearing reduction to inputs by construction

full rationale

The paper introduces non-minimal inflaton-gravity coupling and a complex spectator scalar, then computes the resulting baryon asymmetry from the modified decay channels and reheating dynamics. The abstract states that the asymmetry is obtained from these extensions and is reported as consistent with observations in one case and below in the other. No quoted equations or self-citations reduce the central yield to a fitted parameter renamed as a prediction, nor does any step define the output via the input by construction. The skeptic concern addresses dynamical back-reaction and approximation validity rather than circularity in the derivation chain itself. The result is therefore treated as independently derived from the stated model.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive extraction; typical free parameters in such models include coupling strengths and mass scales chosen to match observed asymmetry.

free parameters (2)
  • non-minimal coupling strength
    Controls effective inflaton mass and decay branching; value implicitly chosen to produce observed baryon asymmetry.
  • biquadratic coupling constant
    Determines interaction strength between spectator and inflaton; adjusted to enhance asymmetry.
axioms (1)
  • domain assumption Standard assumptions of spontaneous baryogenesis during reheating hold.
    Invoked to link inflaton decay to baryon asymmetry generation.

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Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

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