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arxiv: 2606.18095 · v1 · pith:MAIFDUAVnew · submitted 2026-06-16 · 🌌 astro-ph.CO · hep-th

Large primordial non-Gaussianity from transient turns in Higgs-R² inflation

Flavio Pineda , Luis O. Pimentel This is my paper

Pith reviewed 2026-06-26 23:18 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-th
keywords primordial non-GaussianityHiggs-R2 inflationmultifield inflationhyperbolic field spaceisocurvature perturbationstransient turnssuperhorizon evolutionCMB constraints
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The pith

Transient turns in Higgs-R² inflation generate large local non-Gaussianity by transferring isocurvature to adiabatic modes.

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

The paper examines how transient turning trajectories arise in the two-field Higgs-R² inflation model within a hyperbolic field space. It computes the complete bispectrum by tracking the full superhorizon evolution of curvature and isocurvature perturbations without slow-roll or local approximations. The authors demonstrate that these turns efficiently convert isocurvature fluctuations into the adiabatic sector, producing observable local non-Gaussianity. For the benchmark choice of Higgs nonminimal coupling 0.1 and quartic coupling 10 to the minus 10, the local f_NL reaches approximately minus 17.7. Larger values of the nonminimal coupling suppress the turns, recovering the single-field limit where f_NL approaches the small Maldacena consistency value.

Core claim

In multifield Higgs-R² inflation, transient turns in the hyperbolic field space efficiently transfer isocurvature fluctuations into the adiabatic sector and generate sizeable local non-Gaussianities. For a benchmark Higgs nonminimal coupling ξ_h = 0.1 and quartic coupling λ = 10^{-10}, the calculation yields f_NL^loc ≃ -17.7. As the nonminimal coupling increases, the turning rate is suppressed and the model approaches the effective single-field attractor, recovering the Maldacena consistency relation f_NL → 0.0159. Primordial non-Gaussianity therefore provides a sensitive probe of the Higgs nonminimal coupling and can significantly restrict the viable parameter space.

What carries the argument

Transient turning trajectories in the hyperbolic field space manifold, which drive the transfer of isocurvature fluctuations into the adiabatic sector over superhorizon scales.

If this is right

  • For ξ_h = 0.1 and λ = 10^{-10} the model predicts f_NL^loc ≃ -17.7, which lies within reach of current and near-future CMB bounds.
  • Increasing ξ_h progressively reduces the turning rate and drives f_NL toward the single-field consistency value of 0.0159.
  • The full bispectrum calculation without slow-roll approximations reveals efficient isocurvature-to-adiabatic transfer on superhorizon scales.
  • Primordial non-Gaussianity measurements can exclude regions of the Higgs nonminimal coupling and quartic coupling parameter space.

Where Pith is reading between the lines

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

  • The same transfer mechanism may operate in other multifield models that possess a hyperbolic field-space geometry, even when the turns are brief.
  • Improved constraints on f_NL from future CMB experiments could map out the boundary between multifield and single-field regimes in this class of models.
  • The numerical method used here could be applied to compute higher-order statistics such as the trispectrum in the same transient-turn regime.

Load-bearing premise

The field-space geometry remains exactly hyperbolic and the numerical integration of the full superhorizon evolution of curvature and isocurvature modes is free of slow-roll or local approximations.

What would settle it

A CMB measurement of the local non-Gaussianity parameter f_NL^loc that is inconsistent with approximately -17.7 for the benchmark parameters ξ_h = 0.1 and λ = 10^{-10}, or that shows no dependence on the nonminimal coupling when the turning rate is predicted to vary.

read the original abstract

We investigate the generation of primordial non-Gaussianities in multifield Higgs--$R^2$ inflation, focusing on the effects of transient turning trajectories in the hyperbolic field space manifold. We compute the full bispectrum without relying on slow-roll or local approximations and follow the complete superhorizon evolution of curvature and isocurvature perturbations. We show that transient turns efficiently transfer isocurvature fluctuations into the adiabatic sector, generating sizeable local non-Gaussianities. For a benchmark Higgs nonminimal coupling $\xi_h = 0.1$ and quartic coupling $\lambda = 10^{-10}$, we obtain $f_{\rm NL}^{\rm loc}\simeq -17.7$. As the Higgs nonminimal coupling increases, the turning rate is progressively suppressed and the model approaches the effective single-field attractor, recovering the Maldacena consistency relation $f_{\rm NL}\rightarrow 0.0159$. Comparing our predictions with current CMB constraints, we find that primordial non-Gaussianity provides a sensitive probe of the Higgs nonminimal coupling and can significantly restrict the viable parameter space of the model.

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 / 1 minor

Summary. The paper studies primordial non-Gaussianity in multifield Higgs-R² inflation arising from transient turns in a hyperbolic field-space geometry. It reports a numerical computation of the full bispectrum that evolves curvature and isocurvature modes through the entire superhorizon regime without slow-roll or local approximations. For the benchmark point ξ_h = 0.1 and λ = 10^{-10} the local bispectrum yields f_NL^loc ≃ -17.7; the turning rate is suppressed at larger ξ_h and the model recovers the single-field Maldacena consistency relation f_NL → 0.0159. The result is compared with current CMB bounds to argue that non-Gaussianity can constrain the viable range of the Higgs non-minimal coupling.

Significance. If the numerical integration is robust, the work supplies a concrete, falsifiable example of efficient isocurvature-to-adiabatic transfer producing |f_NL^loc| ≳ 10 in a motivated two-field model. The explicit recovery of the consistency relation at large ξ_h constitutes an internal consistency check. The claim that non-Gaussianity can meaningfully restrict the parameter space would be of interest to both inflation model-builders and CMB observers.

major comments (2)
  1. [computation-method paragraph] Computation-method paragraph (abstract): the central numerical result f_NL^loc ≃ -17.7 is obtained from a full superhorizon integration of the bispectrum, yet no convergence tests with respect to time-step size, total number of e-folds, ultraviolet mode cutoff, or gauge-fixing choices are reported; without these diagnostics it is impossible to bound possible accumulated phase or amplitude errors that could affect the reported transfer efficiency.
  2. [abstract] Abstract and benchmark paragraph: the quoted value f_NL^loc ≃ -17.7 is presented without an accompanying error budget or sensitivity analysis to integrator tolerances; because this single number is used both to claim “sizeable” non-Gaussianity and to compare with CMB constraints, the absence of quantified numerical uncertainty is load-bearing for the main conclusion.
minor comments (1)
  1. [abstract] The abstract writes f_{\rm NL}^{\rm loc}\simeq -17.7; if the numerical pipeline can supply a statistical or systematic uncertainty, it should be quoted alongside the central value.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the detailed comments on numerical robustness. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Computation-method paragraph (abstract): the central numerical result f_NL^loc ≃ -17.7 is obtained from a full superhorizon integration of the bispectrum, yet no convergence tests with respect to time-step size, total number of e-folds, ultraviolet mode cutoff, or gauge-fixing choices are reported; without these diagnostics it is impossible to bound possible accumulated phase or amplitude errors that could affect the reported transfer efficiency.

    Authors: We agree that explicit convergence diagnostics strengthen the reliability of the numerical results. In the revised manuscript we will add a dedicated subsection (or appendix) presenting convergence tests varying the integrator time step, total number of superhorizon e-folds, ultraviolet mode cutoff, and gauge-fixing parameters. These tests will show that f_NL^loc remains stable to within a few percent, thereby bounding possible accumulated errors. revision: yes

  2. Referee: Abstract and benchmark paragraph: the quoted value f_NL^loc ≃ -17.7 is presented without an accompanying error budget or sensitivity analysis to integrator tolerances; because this single number is used both to claim “sizeable” non-Gaussianity and to compare with CMB constraints, the absence of quantified numerical uncertainty is load-bearing for the main conclusion.

    Authors: We accept this criticism. The revised version will include a quantified error estimate for the benchmark value, derived from the convergence tests described above, together with a brief sensitivity analysis to integrator tolerances. This will be stated both in the abstract and in the main text when the result is compared with CMB bounds. revision: yes

Circularity Check

0 steps flagged

No significant circularity in numerical bispectrum computation

full rationale

The paper computes the bispectrum by direct numerical integration of the full superhorizon perturbation equations in the Higgs-R^2 model with exactly hyperbolic field-space geometry. The reported f_NL^loc ≃ -17.7 for benchmark parameters (ξ_h=0.1, λ=10^{-10}) is an output of that integration, not a fitted quantity renamed as prediction or a self-defined result. The approach to the Maldacena consistency relation at large ξ_h is a consistency check against an independent single-field result rather than a forced reduction. No load-bearing self-citations, ansatze smuggled via citation, or uniqueness theorems from the authors' prior work are invoked to justify the central claim. The derivation is self-contained against the model equations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

From the abstract alone the model rests on the standard assumptions of multifield inflation plus the specific choice of a hyperbolic field-space metric and the validity of the numerical superhorizon integration; no additional free parameters beyond the two benchmark values are visible.

free parameters (2)
  • ξ_h = 0.1
    Benchmark nonminimal coupling chosen to illustrate the turning effect.
  • λ = 10^{-10}
    Benchmark quartic self-coupling chosen for the numerical example.
axioms (2)
  • domain assumption Field space is a hyperbolic manifold
    Invoked when describing the turning trajectories.
  • domain assumption Full superhorizon evolution of curvature and isocurvature modes can be integrated numerically without slow-roll or local approximations
    Stated as the method used to obtain the bispectrum.

pith-pipeline@v0.9.1-grok · 5728 in / 1469 out tokens · 39081 ms · 2026-06-26T23:18:34.256273+00:00 · methodology

discussion (0)

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