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arxiv: 2604.11068 · v1 · submitted 2026-04-13 · ✦ hep-ph · astro-ph.CO

Radiatively Corrected Hybrid Inflation: Parameter Scans and Machine Learning with ACT and Future CMB Experiments

Waqas Ahmed , Saleh O. Allehabi , Mansoor Ur Rehman This is my paper

Pith reviewed 2026-05-10 16:05 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO
keywords hybrid inflationone-loop correctionsspectral indextensor-to-scalar ratioright-handed neutrinosmachine learningleptogenesisCMB observations
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The pith

One-loop quantum corrections flatten the hybrid inflation potential to produce a red-tilted spectrum consistent with ACT and Planck data.

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

The paper examines a non-supersymmetric hybrid inflation model that incorporates right-handed neutrinos for reheating. At tree level the potential produces a blue-tilted scalar spectrum ruled out by current observations. One-loop corrections from the inflaton-neutrino couplings flatten the potential at large field values, yielding a red spectral index and a suppressed tensor-to-scalar ratio that match data. The model stays within sub-Planckian fields to preserve effective-field-theory control and naturally supports efficient reheating plus non-thermal leptogenesis. A multi-output random forest scan shows roughly fifteen percent of the parameter space satisfies at least one experimental bound.

Core claim

Including one-loop quantum corrections, arising from generic couplings required for reheating, significantly modifies the potential, flattening it at large field values. This leads to a red-tilted spectral index (n_s < 1) and a suppressed tensor-to-scalar ratio r, both consistent with observational constraints. The analysis is restricted to sub-Planckian field values where the effective theory remains valid.

What carries the argument

The one-loop corrected inflaton potential arising from couplings to right-handed neutrinos, which flattens the potential at large field values and shifts the predictions from blue to red tilt.

Load-bearing premise

That the one-loop corrections generated by the inflaton couplings to right-handed neutrinos dominate the potential shape and are computed accurately enough to produce a red tilt while keeping the field values sub-Planckian.

What would settle it

A future measurement showing a spectral index greater than one, or a tensor-to-scalar ratio larger than the suppressed values obtained from the corrected potential, would rule out the radiatively corrected model.

Figures

Figures reproduced from arXiv: 2604.11068 by Mansoor Ur Rehman, Saleh O. Allehabi, Waqas Ahmed.

Figure 1
Figure 1. Figure 1: FIG. 1: The left and right panels illustrate the relationship between the tensor-to-scalar ratio [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The upper-left panel displays the relationship between the mass parameter [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Pairwise overlaps between compatibility regions for current and future CMB experiments. [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Feature importance analysis from Random Forest classifier. The radiative correction parameter [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
read the original abstract

We investigate a realistic non-supersymmetric hybrid inflation model incorporating right-handed neutrinos and assess its viability in light of recent cosmological observations. At tree level, the inflaton potential yields a blue-tilted scalar spectrum, which is disfavored by current data from Planck and ACT that instead support a red tilt. We show that including one-loop quantum corrections, arising from generic couplings required for reheating, significantly modifies the potential, flattening it at large field values. This leads to a red-tilted spectral index ($n_s < 1$) and a suppressed tensor-to-scalar ratio $r$, both consistent with observational constraints. To ensure theoretical control, we focus on sub-Planckian field values, where the effective field theory description remains valid. The coupling of the inflaton to right-handed neutrinos naturally facilitates efficient reheating and enables the generation of the baryon asymmetry via non-thermal leptogenesis. We further explore the model's parameter space using a multi-output random forest classifier, achieving prediction accuracies in the range of $87.5\%$ to $98.9\%$. Our analysis shows that approximately $15\%$ of the parameter space satisfies at least one current experimental constraint, underscoring the essential role of quantum corrections in reconciling particle physics models with precision cosmology, and highlighting the effectiveness of machine learning techniques in probing complex theoretical frameworks.

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

3 major / 2 minor

Summary. The manuscript analyzes a non-supersymmetric hybrid inflation model with right-handed neutrinos. At tree level the potential produces a blue-tilted spectrum disfavored by Planck and ACT data. The authors claim that one-loop Coleman-Weinberg corrections generated by the inflaton–neutrino Yukawa couplings flatten the potential at large but sub-Planckian field values, yielding a red spectral index n_s < 1 and suppressed tensor-to-scalar ratio r that lie inside current observational bounds. Efficient reheating and non-thermal leptogenesis follow from the same couplings. Parameter-space viability is explored with a multi-output random-forest classifier trained on simulated data, reported accuracies range from 87.5 % to 98.9 %, and roughly 15 % of the scanned points satisfy at least one experimental constraint.

Significance. If the one-loop flattening is both dominant and correctly computed, the work supplies a concrete, non-supersymmetric mechanism that reconciles hybrid inflation with precision CMB data while preserving sub-Planckian excursions and incorporating realistic reheating. The machine-learning scan demonstrates a practical route to mapping high-dimensional parameter spaces in inflationary models; the reported accuracies and viable fraction quantify the model’s flexibility under current and future constraints.

major comments (3)
  1. [radiative corrections section] The central claim that one-loop corrections flatten the tree-level hybrid potential sufficiently to produce n_s < 1 and small r at sub-Planckian φ rests on the explicit form and magnitude of the Coleman-Weinberg term. The manuscript must display the full one-loop effective potential (including the fermionic sign, field-dependent mass thresholds, and cutoff regularization) and demonstrate numerically or analytically that this term overcomes the positive tree-level slope inside the EFT regime; without this explicit comparison the reconciliation with ACT/Planck data remains unverified.
  2. [machine learning and parameter scans section] The random-forest classifier achieves 87.5–98.9 % accuracy on labels defined by the same n_s and r observational windows used to assess viability. This introduces a circularity: the network is effectively learning the boundaries of the data cuts rather than independently testing the model’s predictive power. A non-circular test—e.g., training on a subset of constraints and validating on an independent observable such as the reheating temperature or leptogenesis yield—would be required to substantiate the claim that the classifier meaningfully explores the viable parameter space.
  3. [model setup and potential] The assertion that the inflaton–neutrino couplings generate the dominant correction must be justified by comparing the size of the Yukawa-induced loop term against possible contributions from other sectors (e.g., gauge or scalar loops) at the relevant field values. If competing corrections are comparable or larger, the flattening mechanism and the resulting red tilt are no longer guaranteed.
minor comments (2)
  1. [abstract and results] The abstract states that the model is consistent with “observational constraints” but does not quote the specific ACT or Planck bounds (e.g., n_s = 0.9649 ± 0.0042) used to define viability; these numerical thresholds should appear explicitly when the 15 % viable fraction is reported.
  2. [throughout] Notation for the inflaton field and the right-handed neutrino Yukawa coupling should be standardized throughout; occasional use of different symbols for the same quantity obscures the mapping between the analytic potential and the numerical scan.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We have carefully considered each major point and provide point-by-point responses below. Where revisions are needed, we will incorporate the suggested improvements in the revised version of the paper.

read point-by-point responses

  1. Referee: [radiative corrections section] The central claim that one-loop corrections flatten the tree-level hybrid potential sufficiently to produce n_s < 1 and small r at sub-Planckian φ rests on the explicit form and magnitude of the Coleman-Weinberg term. The manuscript must display the full one-loop effective potential (including the fermionic sign, field-dependent mass thresholds, and cutoff regularization) and demonstrate numerically or analytically that this term overcomes the positive tree-level slope inside the EFT regime; without this explicit comparison the reconciliation with ACT/Planck data remains unverified.

    Authors: We agree with the referee that an explicit display and verification of the one-loop effective potential is essential to substantiate our claims. In the revised manuscript, we will present the full Coleman-Weinberg one-loop correction, explicitly including the negative sign from the fermionic loops, the field-dependent mass thresholds for the right-handed neutrinos, and details of the cutoff regularization scheme employed. Furthermore, we will include a numerical demonstration, such as a plot or table, comparing the magnitude of the loop term to the tree-level potential slope at sub-Planckian field values, confirming that the corrections indeed flatten the potential sufficiently to yield n_s < 1 and small r consistent with ACT and Planck data. revision: yes

  2. Referee: [machine learning and parameter scans section] The random-forest classifier achieves 87.5–98.9 % accuracy on labels defined by the same n_s and r observational windows used to assess viability. This introduces a circularity: the network is effectively learning the boundaries of the data cuts rather than independently testing the model’s predictive power. A non-circular test—e.g., training on a subset of constraints and validating on an independent observable such as the reheating temperature or leptogenesis yield—would be required to substantiate the claim that the classifier meaningfully explores the viable parameter space.

    Authors: We appreciate the referee highlighting the issue of circularity in our machine learning approach. Although the random forest is trained on parameters that determine n_s and r through the model's dynamics, we recognize that validating against the same observables used for labeling could limit the independence of the test. To address this, we will revise the manuscript to include a non-circular validation procedure: the classifier will be trained on a subset of the constraints and its performance evaluated on independent observables, specifically the reheating temperature and the baryon asymmetry from non-thermal leptogenesis. This will demonstrate that the viable parameter regions identified also satisfy these additional physical requirements. revision: yes

  3. Referee: [model setup and potential] The assertion that the inflaton–neutrino couplings generate the dominant correction must be justified by comparing the size of the Yukawa-induced loop term against possible contributions from other sectors (e.g., gauge or scalar loops) at the relevant field values. If competing corrections are comparable or larger, the flattening mechanism and the resulting red tilt are no longer guaranteed.

    Authors: We thank the referee for this suggestion to strengthen the justification of our mechanism. In the revised manuscript, we will add a dedicated subsection or paragraph comparing the magnitudes of the different loop contributions at the relevant inflationary field values. We will argue and show numerically that the Yukawa-induced fermionic loops from the inflaton-right-handed neutrino couplings dominate over gauge boson loops and scalar loops, owing to the relatively large Yukawa couplings necessary for efficient reheating and leptogenesis, while the gauge couplings are smaller and the scalar potential parameters are chosen such that their loop effects remain subdominant within the EFT validity range. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives the flattening effect from an explicit one-loop Coleman-Weinberg correction generated by the inflaton–right-handed-neutrino Yukawa couplings that are independently required for reheating and leptogenesis. This correction is computed from standard QFT rules and alters the tree-level hybrid potential in a manner that produces ns < 1 and small r at sub-Planckian values; the result follows from the sign and magnitude of the fermionic loop term rather than from any redefinition or fit to the target observables. The subsequent random-forest scan is a post-processing tool that labels points according to the same external constraints and reports classifier accuracy on held-out simulated data; the 15 % viable fraction is an output of that scan, not a premise used to derive the potential modification itself. No equation or claim reduces by construction to its own input, no self-citation supplies a uniqueness theorem, and the central slow-roll predictions remain independently falsifiable against Planck/ACT data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated in sufficient detail to populate the ledger.

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