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arxiv: 2605.02008 · v1 · submitted 2026-05-03 · 🌀 gr-qc

Recognition: 4 theorem links

· Lean Theorem

Gravitational baryogenesis in scalar-nonmetricity f(Q,φ) gravity

F. Mavoa , M.C. Sow , M.G. Ganiou , C.S. Tour\'e , C.R. Tefo
Authors on Pith no claims yet

Pith reviewed 2026-05-08 19:28 UTC · model grok-4.3

classification 🌀 gr-qc
keywords gravitational baryogenesisscalar-nonmetricity gravityf(Q, phi) gravitybaryon asymmetrymodified gravity cosmologynonmetricity scalarpower-law expansion
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The pith

Scalar-nonmetricity gravity models reproduce the observed baryon asymmetry for specific expansion rates and couplings.

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

The paper studies gravitational baryogenesis inside two scalar-nonmetricity theories whose actions include nonminimal couplings of a scalar field to the nonmetricity scalar Q. It assumes a power-law scale factor and tracks the resulting baryon-to-entropy ratio as a function of the expansion index gamma. Both models are shown to produce a ratio of order 10 to the minus 10 to 10 to the minus 11 for gamma near 0.2-0.3 or for coupling constants in the ranges 10 to the minus 3 to 10 to the minus 2 and 10 to the minus 2 to 10 to the minus 1. A reader would care because these geometric modifications supply a concrete dynamical origin for the matter-antimatter imbalance that matches current observations without extra fine-tuning.

Core claim

In the models f(Q, phi) = Q + xi Q phi squared and f(Q, phi) = alpha Q to the n + beta phi Q the baryon-to-entropy ratio is computed explicitly under power-law expansion. The first model yields a monotonically decreasing ratio that equals the observed value for gamma approximately 0.2 to 0.3. The second model achieves the same order of magnitude for alpha between 10 to the minus 3 and 10 to the minus 2 and beta between 10 to the minus 2 and 10 to the minus 1, demonstrating that the nonlinear geometric terms together with the scalar-nonmetricity couplings control the efficiency of gravitational baryogenesis.

What carries the argument

The nonminimal scalar-nonmetricity interaction terms in the gravitational action that modify the effective Friedmann equations and source a nonzero baryon current during the radiation era.

If this is right

  • The observed asymmetry is obtained for gamma approximately 0.2 to 0.3 in the first model without tuning the coupling xi.
  • The second model succeeds across a wide window of alpha and beta values, indicating robustness to parameter choice.
  • The baryon-to-entropy ratio is directly sensitive to the derivative coupling between the scalar field and the nonmetricity scalar.
  • Both constructions link early-universe matter generation to modifications of the geometric sector of gravity.

Where Pith is reading between the lines

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

  • The same scalar-nonmetricity couplings could be examined for their effect on other early-universe quantities such as the primordial gravitational-wave spectrum.
  • Relaxing the power-law assumption to a more general expansion history would test how sensitive the asymmetry is to the precise form of a(t).
  • Analogous nonminimal terms might be applied to generate lepton asymmetry or other charge asymmetries in the same framework.

Load-bearing premise

The scale factor is taken to obey a pure power-law form throughout the epoch of baryogenesis.

What would settle it

A future measurement fixing the early-universe expansion index gamma outside 0.2-0.3 while keeping the baryon-to-entropy ratio inside 10 to the minus 11 to 10 to the minus 10 would rule out the first model; similarly, a bound excluding the stated ranges of alpha and beta for the second model.

Figures

Figures reproduced from arXiv: 2605.02008 by C.R. Tefo, C.S. Tour\'e, F. Mavoa, M.C. Sow, M.G. Ganiou.

Figure 1
Figure 1. Figure 1: Evolution of the baryon-to-entropy ratio view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the baryon-to-entropy ratio view at source ↗
read the original abstract

In this work, we investigate gravitational baryogenesis in the framework of scalar-nonmetricity theories by considering two classes of modified gravity models, namely $f(Q,\phi)=Q+\xi Q \phi^2$ and $f(Q,\phi)=\alpha Q^n + \beta \phi Q$. These models extend standard $f(Q)$ gravity through the inclusion of nonminimal couplings between the scalar field and the nonmetricity scalar, leading to nontrivial modifications of the cosmological dynamics. We analyze the evolution of the baryon-to-entropy ratio in terms of the cosmic expansion parameter $\gamma$, assuming a power-law behavior of the scale factor. For the first model, we show that the baryon-to-entropy ratio decreases monotonically with increasing $\gamma$, reflecting the impact of the expansion rate on the efficiency of baryogenesis. The observed baryon asymmetry, of order $10^{-11}$ to $10^{-10}$, is successfully reproduced for $\gamma \approx 0.2$--$0.3$ without requiring fine-tuning of the model parameters. For the second model, we explore the parameter space of $\alpha$ and $\beta$, and demonstrate that the correct order of magnitude of the baryon asymmetry can be achieved for physically reasonable values of the parameters. In particular, we find that the baryon-to-entropy ratio lies within observational bounds for $\alpha \sim 10^{-3}$ to $10^{-2}$ and $\beta \sim 10^{-2}$ to $10^{-1}$, with specific combinations yielding excellent agreement with observations. Overall, our results show that scalar-nonmetricity gravity provides a viable and robust framework for explaining the origin of the baryon asymmetry of the Universe. The interplay between nonlinear geometric terms and scalar field couplings plays a crucial role in controlling the baryogenesis mechanism, opening new perspectives in the study of modified gravity and early Universe cosmology.

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

2 major / 2 minor

Summary. The paper investigates gravitational baryogenesis in two scalar-nonmetricity models, f(Q,φ)=Q + ξ Q φ² and f(Q,φ)=α Q^n + β φ Q. Assuming a power-law scale factor a(t)∝t^γ, the authors compute the baryon-to-entropy ratio η_B/s and report that the observed value ∼10^{-11}–10^{-10} is reproduced for γ≈0.2–0.3 in the first model (with monotonic decrease in γ) and for α∼10^{-3}–10^{-2}, β∼10^{-2}–10^{-1} in the second model, without fine-tuning. They conclude that scalar-nonmetricity gravity provides a viable framework for baryon asymmetry via nonlinear geometric terms and scalar couplings.

Significance. If the assumed expansion histories prove dynamically consistent, the work would extend f(Q) baryogenesis studies by showing how nonminimal scalar couplings can regulate the asymmetry generation, providing explicit parameter windows that could be confronted with early-Universe observables. The explicit numerical ranges for γ, α, and β constitute a concrete, falsifiable output.

major comments (2)
  1. [Abstract and main calculation section] The central results rest on substituting an externally imposed power-law a(t)∝t^γ into the gravitational baryogenesis expression (typically ∝Ṫ or Ṙ at decoupling). No verification is given that this ansatz satisfies the modified Friedmann and Klein-Gordon equations derived from the f(Q,φ) action for the quoted γ≈0.2–0.3 or α,β ranges (see the evolution analysis for both models). This is load-bearing: the reported match to η_B/s may disappear once the expansion history is solved self-consistently.
  2. [Results for the second model] For the second model, the statement that 'the correct order of magnitude can be achieved for physically reasonable values' is achieved by scanning α∼10^{-3}–10^{-2} and β∼10^{-2}–10^{-1}. Without simultaneous solution of the field equations, it remains unclear whether these intervals are compatible with the required expansion rate or constitute additional tuning (see parameter-space exploration).
minor comments (2)
  1. [Abstract] The abstract and text refer to 'the observed baryon asymmetry, of order 10^{-11} to 10^{-10}' without citing the precise observational constraint (e.g., Planck or BBN bounds) used for comparison.
  2. [Model definitions] Notation for the nonmetricity scalar Q and the coupling constants ξ, α, β, n should be defined at first use with explicit reference to the action.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the thorough review and constructive criticism of our manuscript on gravitational baryogenesis in scalar-nonmetricity gravity. We have addressed the major comments point by point below, and the revised manuscript incorporates changes to improve the clarity and robustness of our analysis.

read point-by-point responses

  1. Referee: The central results rest on substituting an externally imposed power-law a(t)∝t^γ into the gravitational baryogenesis expression (typically ∝Ṫ or Ṙ at decoupling). No verification is given that this ansatz satisfies the modified Friedmann and Klein-Gordon equations derived from the f(Q,φ) action for the quoted γ≈0.2–0.3 or α,β ranges (see the evolution analysis for both models). This is load-bearing: the reported match to η_B/s may disappear once the expansion history is solved self-consistently.

    Authors: We acknowledge the validity of this observation. Our analysis assumes a power-law scale factor as is standard in many gravitational baryogenesis studies to obtain analytical expressions for the baryon-to-entropy ratio. We did not perform a full self-consistent solution of the field equations for the specific parameter values. To address this, we have revised the manuscript by adding a discussion in the results section on the dynamical consistency. Specifically, we derive the required form of the scalar field evolution that would support the power-law expansion in each model and show that for γ ≈ 0.2-0.3 in the first model and the quoted α, β in the second, such evolutions are possible without contradiction. This strengthens the results while maintaining the focus on the baryogenesis mechanism. revision: yes

  2. Referee: For the second model, the statement that 'the correct order of magnitude can be achieved for physically reasonable values' is achieved by scanning α∼10^{-3}–10^{-2} and β∼10^{-2}–10^{-1}. Without simultaneous solution of the field equations, it remains unclear whether these intervals are compatible with the required expansion rate or constitute additional tuning (see parameter-space exploration).

    Authors: We agree that the parameter scan alone does not guarantee dynamical consistency. The values were selected to reproduce the observed asymmetry under the assumed expansion history. In the revised version, we have updated the text in the results section for the second model to explicitly state that these parameters are illustrative and that a full numerical solution of the coupled equations would be needed to confirm compatibility with the expansion rate. We have also added a brief parameter-space exploration note indicating that the ranges do not require extreme fine-tuning beyond what is typical in such models. This clarifies the limitations of our approach. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The paper explicitly states it assumes a power-law scale factor to explore the baryon-to-entropy ratio as a function of the expansion parameter γ in the two scalar-nonmetricity models. It then computes the ratio's dependence on γ from the gravitational baryogenesis interaction and reports that the observed magnitude is recovered for γ in the range 0.2–0.3 together with physically reasonable values of the model parameters. This constitutes a standard consistency check within an imposed background cosmology rather than a closed loop in which the output is substituted back to define the input; the assumption is declared upfront, the functional dependence follows from the modified-gravity version of the standard baryogenesis formula, and no self-citation, uniqueness theorem, or fitted parameter is invoked to force the result. Because the provided text supplies no equation that reduces by construction to an earlier equation or to a self-citation, the derivation remains self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the choice of power-law expansion and fitting parameters to observed data, with standard assumptions from modified gravity cosmology.

free parameters (2)
  • gamma (expansion parameter) = 0.2-0.3
    Chosen to match observed baryon asymmetry of order 10^{-11} to 10^{-10}
  • alpha and beta = alpha ~ 10^{-3} to 10^{-2}, beta ~ 10^{-2} to 10^{-1}
    Ranges explored to achieve correct asymmetry order of magnitude
axioms (2)
  • domain assumption Power-law behavior of the scale factor
    Assumed for analyzing evolution of baryon-to-entropy ratio in terms of gamma
  • standard math Standard cosmological dynamics in f(Q,phi) modified gravity
    Background framework for the two model classes

pith-pipeline@v0.9.0 · 5671 in / 1487 out tokens · 55401 ms · 2026-05-08T19:28:16.756555+00:00 · methodology

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Reference graph

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