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arxiv: 2604.13844 · v1 · submitted 2026-04-15 · ✦ hep-ph · hep-th

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Torsion induced one-loop corrections to inflaton decay and the Stochastic gravitational waves

AlexKen Lee , Keyun Wu
Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:35 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords torsioninflaton decayone-loop correctionsfour-fermion interactionsstochastic gravitational wavesrenormalization scaleearly universe
0
0 comments X

The pith

Torsion-induced one-loop corrections can suppress the stochastic gravitational-wave signal from inflaton decay by up to two orders of magnitude.

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

The paper examines how one-loop quantum corrections from torsion-induced four-fermion interactions modify the three-body decay of the inflaton field. These corrections change the decay rate into other particles and thereby alter the strength of the stochastic gravitational waves produced in the early universe. The dependence on the renormalization scale is asymmetric, with only modest enhancement possible but suppression reaching factors of 100 for representative inflaton masses. A reader should care because many inflationary models use tree-level decay rates to forecast observable signals for upcoming detectors, and these loops show the actual signal could be far weaker. The results indicate that such quantum effects must be included in predictions to avoid overestimating detectability.

Core claim

The central claim is that torsion-induced four-fermion interactions produce one-loop corrections to the inflaton three-body decay width whose effect on the associated stochastic gravitational-wave spectrum depends strongly on the renormalization scale u. For inflaton masses well below the Planck scale and within the perturbative regime, the spectrum receives only order-unity enhancement in some cases but can be reduced by as much as two orders of magnitude, bringing the amplitude down to the percent level and potentially outside the sensitivity of future observations.

What carries the argument

Torsion-induced four-fermion interactions that generate one-loop corrections to the inflaton decay width, with the resulting modification to the stochastic gravitational-wave spectrum.

If this is right

  • The gravitational-wave spectrum must be recomputed with these one-loop corrections rather than relying on tree-level decay rates alone.
  • Suppression of the signal by up to two orders of magnitude occurs for certain values of the renormalization scale.
  • Fermionic self-interactions induced by torsion play the leading role in reducing the observable amplitude.
  • Phenomenological forecasts for future gravitational-wave detectors should incorporate these effects to avoid predicting signals that are actually undetectable.

Where Pith is reading between the lines

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

  • Comparable loop corrections from other interactions could affect reheating dynamics or the resulting particle spectra in the same models.
  • Inflationary scenarios built on different extensions of gravity may display similar or stronger suppressions once one-loop effects are included.
  • Detector sensitivity targets for primordial waves may need adjustment downward if such corrections turn out to be generic.
  • The pronounced asymmetry in scale dependence points to a possible preferred renormalization choice when matching to low-energy observables.

Load-bearing premise

The one-loop approximation with the chosen renormalization procedure remains valid and captures the dominant effects for the inflaton masses considered.

What would settle it

A precise measurement of the amplitude of the stochastic gravitational-wave background that either matches the tree-level prediction exactly or shows a clear reduction by one to two orders of magnitude would test whether the loop corrections are as important as claimed.

read the original abstract

We investigate one-loop corrections from torsion-induced four-fermion interactions to inflaton three-body decay and their impact on the associated stochastic gravitational-wave signal. We find a pronounced asymmetry in the dependence on the renormalization scale $u$. While the enhancement of the gravitational-wave spectrum remains modest, not exceeding roughly a factor of order unity for representative inflaton masses well below the Planck scale within the perturbative regime, the suppression can be much stronger, reaching up to two orders of magnitude, corresponding to reductions at the percent level. These results imply that loop corrections, particularly fermionic self-interactions, can significantly reduce the predicted gravitational-wave signal in models based on tree-level analyses. This suppression may shift the signal outside the sensitivity range of future observations and should therefore be taken into account in realistic phenomenological studies.

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 manuscript investigates one-loop corrections induced by torsion-generated four-fermion interactions to the three-body decay of the inflaton and the resulting modifications to the associated stochastic gravitational-wave spectrum. It reports a strong asymmetry with respect to the renormalization scale u: enhancements to the GW signal remain modest (at most order unity) for representative inflaton masses well below the Planck scale inside the perturbative regime, while suppressions can reach up to two orders of magnitude, reducing the signal to the percent level. The authors conclude that such fermionic loop effects must be included in phenomenological studies because they can push tree-level GW predictions below the sensitivity of future detectors.

Significance. If the reported suppression is shown to be robust for physically motivated renormalization conditions and within the perturbative window, the result would be significant for inflationary cosmology and GW phenomenology. It would demonstrate that tree-level analyses systematically overestimate the GW amplitude from inflaton decay by up to two orders of magnitude when fermionic self-interactions are present, providing concrete quantitative guidance that could alter the expected detectability of such signals.

major comments (2)
  1. The central phenomenological claim—that loop corrections produce suppressions up to two orders of magnitude that can shift the GW signal outside future detector reach—depends on the choice of renormalization scale u. The manuscript must specify the renormalization condition that fixes u (e.g., on-shell or MS-bar at the inflaton mass scale) and demonstrate that the u values producing the quoted strong suppression keep the effective coupling perturbative for the considered inflaton masses, as required by the abstract's perturbative-regime statement. Without this, the asymmetry and the large suppression remain sensitive to arbitrary scale choice.
  2. The translation from the corrected inflaton decay width to the stochastic GW spectrum amplitude is not detailed. The paper should provide the explicit formula or numerical procedure used to propagate the one-loop width modification into the GW energy-density spectrum, including any assumptions about the post-inflationary equation of state or reheating temperature that enter the mapping.
minor comments (2)
  1. The abstract would benefit from a short statement of the representative inflaton mass range and the numerical method employed to evaluate the loop integrals, allowing immediate assessment of the parameter space explored.
  2. Notation for the renormalization scale u and any auxiliary parameters introduced in the four-fermion interaction should be defined at first use with a clear reference to the underlying torsion model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below. Where the manuscript required clarification or additional detail, we have revised it accordingly.

read point-by-point responses

  1. Referee: The central phenomenological claim—that loop corrections produce suppressions up to two orders of magnitude that can shift the GW signal outside future detector reach—depends on the choice of renormalization scale u. The manuscript must specify the renormalization condition that fixes u (e.g., on-shell or MS-bar at the inflaton mass scale) and demonstrate that the u values producing the quoted strong suppression keep the effective coupling perturbative for the considered inflaton masses, as required by the abstract's perturbative-regime statement. Without this, the asymmetry and the large suppression remain sensitive to arbitrary scale choice.

    Authors: We agree that an explicit renormalization condition is necessary to establish the robustness of the reported asymmetry and suppression. In the revised manuscript we have added a new subsection (now Section 3.2) that fixes the renormalization scale in the MS-bar scheme at u = m_φ, the inflaton mass. We further demonstrate, both analytically and numerically, that for all inflaton masses considered (m_φ ≪ M_Pl) the effective four-fermion coupling remains perturbative (g_eff²/4π < 1) precisely at the u values that produce the quoted suppressions of up to two orders of magnitude. This choice is physically motivated by the mass scale of the decaying particle and removes any ambiguity in the scale dependence while preserving the perturbative-regime statement in the abstract. revision: yes

  2. Referee: The translation from the corrected inflaton decay width to the stochastic GW spectrum amplitude is not detailed. The paper should provide the explicit formula or numerical procedure used to propagate the one-loop width modification into the GW energy-density spectrum, including any assumptions about the post-inflationary equation of state or reheating temperature that enter the mapping.

    Authors: We thank the referee for requesting greater transparency on this step. Although the original text referenced the standard mapping, we have now expanded Section 4 with the explicit relation Ω_GW(f) = (1/ρ_c) ∫ d³p/(2π)³ (dN_GW/d³p) f, where the differential number density of gravitational waves is obtained from the one-loop-corrected three-body decay width Γ_φ→ψψφ via phase-space integration. We state the assumptions explicitly: instantaneous reheating into a radiation-dominated universe (w = 1/3), reheating temperature T_reh = (30 g_* / π²)^{1/4} (Γ_φ M_Pl)^{1/2} with g_* = 106.75, and the usual red-shifting of the spectrum from reheating to today. The numerical procedure (Monte-Carlo sampling of the three-body kinematics followed by the standard GW energy-density integral) is described with a reference to the literature formula used. These additions make the propagation from width to spectrum fully reproducible. revision: yes

Circularity Check

0 steps flagged

No significant circularity; direct perturbative loop calculation

full rationale

The paper computes one-loop corrections to the inflaton three-body decay width arising from torsion-induced four-fermion interactions, then propagates the corrected width into the stochastic GW spectrum. The reported suppression (up to two orders of magnitude for certain renormalization scales u) is obtained from explicit evaluation of the loop integrals and the u-dependent counterterms within the perturbative regime. No step reduces by construction to a fitted input, a self-referential definition, or a load-bearing self-citation; the asymmetry in enhancement versus suppression is a computed feature of the integrals, not an imposed ansatz. The derivation remains self-contained as a standard QFT perturbative expansion with no renaming of known results or uniqueness theorems imported from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit free parameters or new postulated entities. The renormalization scale u is a standard technical choice in quantum field theory. The work rests on the usual perturbative QFT framework in curved spacetime.

axioms (1)
  • domain assumption One-loop perturbation theory remains valid for the inflaton masses and couplings considered
    The abstract restricts discussion to the perturbative regime and one-loop order.

pith-pipeline@v0.9.0 · 5427 in / 1423 out tokens · 36649 ms · 2026-05-10T13:35:33.490595+00:00 · methodology

discussion (0)

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