General Relativity and Quantum Cosmology · arXiv:1101.3636 v2 · submitted 19 Jan 2011
Non-Gaussianity Consistency Relation for Multi-field Inflation
The paper says
“We show that multi-field models described by the δN formalism obey an inequality between $f_{\rm NL}$ and one of the local-form {\it trispectrum} amplitudes, $\tau_{\rm NL}$, such that $\tau_{\rm NL}>\frac12(\frac65f_{\rm NL})^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small.”
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Abstract
While detection of the "local form" bispectrum of primordial perturbations would rule out all single-field inflation models, multi-field models would still be allowed. We show that multi-field models described by the δN formalism obey an inequality between $f_{\rm NL}$ and one of the local-form {\it trispectrum} amplitudes, $\tau_{\rm NL}$, such that $\tau_{\rm NL}>\frac12(\frac65f_{\rm NL})^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small. Detection of a violation of this inequality would rule out most of multi-field models, challenging inflation as a mechanism for generating the primoridal perturbations.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.25 · mentions code or data availability 0.01
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| While detection of the "local form" bispectrum of primordial perturbations would rule out all single-field inflation models, multi-field models would still be allowed. | background 0.99 | 0.05 | 0.04 | asserted 0.81 |
| We show that multi-field models described by the $\delta N$ formalism obey an inequality between $f_{\rm NL}$ and one of the local-form {\it trispectrum} amplitudes, $\tau_{\rm NL}$, such that $\tau_{\rm NL}>\frac12(\frac65f_{\rm NL})^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small. | result 0.93 | 0.94 | 0.89 | asserted 1.00 |
| Detection of a violation of this inequality would rule out most of multi-field models, challenging inflation as a mechanism for generating the primoridal perturbations. | interpretation 0.99 | 0.22 | 0.39 | asserted 0.54 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,114 input tokens, $0.0001 reported.
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Cited by 6 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Pushing the Primordial Frontier: Exact Linear Solutions in Multifield Inflation astro-ph.CO · Jun 2026
- Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity astro-ph.CO · Mar 2013
- \delta N Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum astro-ph.CO · Feb 2013
- Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background astro-ph.CO · Feb 2013
- Inflation with an extra light scalar field after Planck astro-ph.CO · Dec 2015
- COrE (Cosmic Origins Explorer) A White Paper astro-ph.CO · Feb 2011
How the literature uses it
24 arXiv papers cite this in 33 sentences
Papers citing it · 25 sentences without a confident label
Contests it 1 paper
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Additionally, it is important to note that the well-known Suyama-Yamaguchi consistency relation [ref] between the three and four point non-Gaussian parameters, $f_NL^local$, $τ_NL^local$ and $g_NL^local$ violates [ref] in the present context due to the appearance of $⋯$ terms in Eq ([ref],[ref],[ref]).
Constraining ${\cal N}=1$ supergravity inflation with non-minimal K\"ahler operators using $\delta N$ formalism · Computation of local type of non-Gaussianity and CMB dipolar asymmetry · contest 0.81
Compares with it 1 paper
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Pln(kL) +(15 2A_3^2 A_1^2 + 2A_3^3 A_2^2 A_1)(Pln(kL))^2 +. 52A_3^4 A_2^2 A_1^2(Pln(kL))^3 ] g_NL^equi. = A_3 A_1^3 N^6 [1+3A_2^2 A_1^2Pln(kL) +(3A_3 A_2^2 A_1^3+32A_3^2 A_1^2)(Pln(kL))^2 +A_3^3 A_1^3(Pln(kL))^3] The expression for $τ_NL^equi.$ is consistent with the one-loop expression given in [ref] .
Local Scale-Dependent Non-Gaussian Curvature Perturbations at Cubic Order · Trispectrum · 0.80
Cites it as background 5 papers
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As a different consistency condition, the Suyama-Yamaguchi (SY) inequality [ref] , [ref] , [ref] between the amplitude of the Bispectrum in the squeezed limit, $f_NL$, and the amplitude of the trispectrum in the collapsed limit, $τ_NL$, are expected to hold generally in models of inflation based on scalar fields.
\delta N Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum · Introduction · 0.86
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See [ref] for further discussions on the loop corrections and the universality of this inequality, and [ref] for an observational attempt to test it from existing observations.
Scale Dependence of the Halo Bias in General Local-Type Non-Gaussian Models I: Analytical Predictions and Consistency Relations · Introduction · 0.80
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One of the interesting theoretical issue about these higher order non-Gaussianities is an inequality between $f_NL$ and $τ_NL$, so-called, Suyama-Yamaguchi inequality [ref] .
Scale-dependent bias with higher order primordial non-Gaussianity: Use of the Integrated Perturbation Theory · Introduction · 0.94
What it cites · 3 sentences without a confident label
Builds on 1 paper
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This result generalizes the Suyama-Yamaguchi inequality (which included only the tree-level terms) as well as Ref. [ref] (which included up to the second-order terms).
On Classification of Models of Large Local-Type Non-Gaussianity · Introduction · 0.80
Uses data or values from 1 paper
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The latest observations give $n_s= 0.96±0.01$ [ref] , which may be taken as evidence for inflation.
The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectra · Introduction · 0.93
Cites as background 1 paper
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Departure from Gaussianity, called non-Gaussianity, has emerged as a powerful test of inflation over the last decade (see [ref] for reviews).
The Pursuit of Non-Gaussian Fluctuations in the Cosmic Microwave Background · Introduction · 0.98
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