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Cited by 178Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesDark Matter and Cosmic Phenomena

The DOI matches its Crossref record; 188 of the 188 references it cites were found in a registry or an index; none of the 65 sources its claims cite is checked for support yet.

Review of Local Non‐Gaussianity from Multifield Inflation

Open access
Byrnes, Christian T., Choi, Ki-Young·2010·Advances in Astronomy
DOI 10.1155/2010/724525
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Abstract

We review models which generate a large non‐Gaussianity of the local form. We first briefly consider three models which generate the non‐Gaussianity either at or after the end of inflation; the curvaton scenario, modulated (p)reheating, and an inhomogeneous end of inflation. We then focus on ways of generating the non‐Gaussianity during inflation. We derive general conditions which a product or sum separable potential must satisfy in order to generate a large local bispectrum during slow‐roll inflation. As an application, we consider two‐field hybrid inflation. We then derive a formalism not based on slow roll which can be applied to models in which the slow‐roll parameters become large before inflation ends. An exactly soluble two‐field model is given in which this happens. Finally, we also consider further non‐Gaussian observables, a scale dependence of fNL and the trispectrum.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

This review surveys multifield inflation models that can generate large local-type primordial non-Gaussianity, covering curvaton, modulated (p)reheating, inhomogeneous end of inflation, and during-inflation mechanisms. It derives conditions for large \(f_{\rm NL}\) in separable slow-roll potentials, applies them to two-field hybrid inflation, and extends the analysis beyond slow roll with an exactly soluble two-field model.

Key findings

  • Local non-Gaussianity can be generated at or after inflation by the curvaton scenario, modulated (p)reheating, and an inhomogeneous end of inflation; during slow-roll multifield inflation it can also be large if the trajectory is almost entirely along one field but the orthogonal field grows by at least an order of magnitude toward the end.
  • For a product separable potential, large \(|f_{\rm NL}|\) requires conditions such as \(\sin^2\theta_* \sin^4\theta_e (1/\sin^2\theta_e G_p -1)\); a quadratic-times-exponential toy model gives \(|f_{\rm NL}|\sim 30\) with \(\phi_*\sim 10^{-3}M_P\) for \(\lambda=0.05\) and \(\chi_*=16M_P\).
  • Two-field hybrid inflation can yield large \(f_{\rm NL}\) for positive, negative, or mixed \(\eta\) parameters; Table 1’s first example (\(\eta_{\phi\phi}=0.04\), \(\eta_{\chi\chi}=-0.04\), \(\phi_*=1\), \(\chi_*=6.8\times10^{-5}\), \(r=1\)) gives \(f_{\rm NL}=-123\), \(\tau_{\rm NL}=4.4\times10^4\), \(g_{\rm NL}=-33\), \(n_\zeta-1=0\), and \(r=0.006\), showing \(|f_{\rm NL}|>100\) with a scale-invariant spectrum is possible.
  • Beyond slow roll, an exact two-field solution with \(\alpha=-100\), \(\beta=20\), \(m=6\), \(n=6/5\), and \(N_{\rm tot}=60\) gives \(f_{\rm NL}\approx58\) from the simplified formula and \(\approx53\) from the full formula, with \(\gamma_\phi=29\) and \(\gamma_\chi=-13\) at the end; the review also notes \(\tau_{\rm NL}\ge(6f_{\rm NL}/5)^2\), WMAP5 bounds \(-7.4<g_{\rm NL}/10^5<8.2\) and \(-0.6<\tau_{\rm NL}/10^4<3.3\) at 95% CL, and scale dependence satisfying \(-4(\eta_{\phi\phi}-\eta_{\chi\chi})<n_{f_{\rm NL}}<0\).

Methods

  • Review and analytic derivation using the \(\delta N\) formalism, with definitions of the power spectrum, bispectrum, \(f_{\rm NL}\), trispectrum parameters \(\tau_{\rm NL}\) and \(g_{\rm NL}\), and the scale dependence \(n_{f_{\rm NL}}\).
  • Slow-roll analysis for sum- or product-separable potentials, deriving general conditions for large local \(f_{\rm NL}\), then applying them to two-field hybrid inflation including waterfall-field end-of-inflation effects.
  • Beyond slow roll, uses first-order Hamilton-Jacobi formalism with a separable Hubble parameter and presents an exact two-field exponential-potential solution, comparing simplified and full \(f_{\rm NL}\) formulas.

Limitations

  • Stated: the paper considers only adiabatic primordial perturbations and neglects secondary non-Gaussianities generated at later times; further evolution after inflation in the hybrid model is model-dependent and “has not been considered in depth”; the exact solution’s potential needs modification after inflation for reheating; initial conditions require fine-tuning.
  • Stated: the curvaton treatment uses a sudden-decay approximation, though it agrees well with full numerical studies; modulated instant preheating models are allowed only in a small corner of parameter space and for special initial conditions.
  • Evident from the text: as a review, it synthesizes prior work and presents no new observational data; numerical examples depend on chosen parameter values and on analytic approximations such as slow roll, separable potentials, or separable Hubble parameter.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1155/2010/724525

Cites

188 of 188 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

0 of 65 cited sources checked · 0 supported · 0 flagged

Show all 86 claims

  • It may state two separate claims as one. 63
  • Probably not a substantial claim. 24
  • The quote only partly states this claim. 4
85 of 85

  • The authors state this as an assumption.

    Inflation ends abruptly by a waterfall field which is heavy during inflation and hence does not affect the dynamics during inflation.

    “We assume that inflation ends abruptly by a waterfall field which is heavy during inflation and hence does not affect the dynamics during inflation.”

  • The authors state this as an assumption.

    The curvaton field decays suddenly on the H = Γ uniform energy-density hypersurface.

    “Assuming the sudden decay of the curvaton field on the H = Γ uniform energydensity hypersurface, that is, when the local Hubble rate equals the decay rate for the curvaton, leads to a nonlinear relation between the local curvaton density and the radiation density before and after the decay”

  • The authors state this as an assumption.

    The transition to the radiation epoch at the end of inflation is quick, so the dynamics of the waterfall field can be neglected.

    “So far, we have assumed a quick transition to the radiation epoch at the end of inflation, thereby neglecting the dynamics of the waterfall field.”

  • The authors state this as an assumption.

    The quantities δ and γ are much smaller than unity at Hubble exit t=t*, so that the δN formalism can be used.

    “We assume that the quantities δ and γ are much smaller than unity at Hubble exit t = t * , in order that we can use the δN formalism.”

  • The authors state this as an assumption.

    The quantities m and n are not too big; they satisfy m,n < R2.

    “We assume that the quantities m and n are not too big.Namely, they satisfy the inequality m, n R 2 .”

  • The authors state this as an assumption.

    The fields have a Gaussian distribution at Hubble exit.

    “assuming that the fields have a Gaussian distribution at Hubble exit”

  • The authors state this as an assumption.

    The local model of non-Gaussianity is assumed when interpreting the WMAP constraint.

    “assuming the local model of non-Gaussianity”

  • The paper relies on this without support.

    The trispectrum (four-point function) depends on two nonlinearity parameters.

    “The trispectrum (four-point function) depends on two nonlinearity parameters.”

  • The paper relies on this without support.

    In general, τ_NL ≥ (6 f_NL /5)^2.

    “In general, τ NL ≥ (6 f NL /5) 2 .”

  • The paper relies on this without support.

    Planck will be able to detect the bispectrum and trispectrum if they are large enough.

    “then both the bispectrum and the trispectrum should be large enough for Planck to detect.”
10 of 10

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Figure 1 gives a different end-of-inflation f NL from the full formula

    Minor

    For the stated example, the text says the full formula gives f NL ≈ 53, while Figure 1 reports f NL ≈ 59 at the end of inflation. Both statements refer to the end-of-inflation value for the example.

  • Table 2 tensor-to-scalar ratio is inconsistent with Table 1 and equation (47)

    Minor

    For the row with ηφφ = 0.02, ηχχ = -0.04, and r = 1, equations (40) and (47) imply that changing the end condition multiplies the Table 1 tensor-to-scalar ratio by 2/1.25 = 1.6. The Table 1 value of 0.002 therefore gives approximately 0.0032, not the 0.026 reported in Table 2.

2 of 2

Citations

Cites

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Research works printed but not linked: 2

  1. Starobinsky A. A., 1985, Mnogokomponentnye de-sitterovskie (inflyatsionnye) stadii i generatsiya vozmushchenii, Pisma Zhurnal Eksperimental′noi i Teoreticheskoi Fiziki, 42, 124
  2. 10.1103/physrevd.77.083511 · DOI · Paper page

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Metadata

Authors
Byrnes, C. T., & Choi, K.-Y.
Affiliations
  • Bielefeld University (DE)
  • Pusan National University (KR)
Corresponding author
Choi, Ki-Young
ORCID
Venue
Advances in Astronomy
Publisher
Wiley
Published
2010-01
Volume
2010
Issue
1
ISSN
  • 1687-7969 (ISSN-L)
  • 1687-7977
DOI
10.1155/2010/724525
OpenAlex
W2120328039
Semantic Scholar
98df8ab56191b74076cc80e705ab8bc9f2686a29
Cited by
178
References
163
Citations by year
2026: 5 · 2025: 9 · 2024: 7 · 2023: 7 · 2022: 7 · 2021: 7 · 2020: 10 · 2019: 3 · 2018: 15 · 2017: 6 · 2016: 9 · 2015: 7 · 2014: 14 · 2013: 20 · 2012: 17
FWCI
12.88
Type
journal article
Language
en
Open access
Licence
Locations
  • Advances in Astronomy (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • PUB – Publications at Bielefeld University (Bielefeld University) (submittedVersion, other-oa)
  • Publikationen an der Universität Bielefeld (Universität Bielefeld) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
Korea Research Foundation (KRF-2008-341-C00008)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
Keywords
local non-Gaussianity, multi-field inflation, curvaton, bispectrum, slow-roll inflation, separable potentials, trispectrum, primordial non-Gaussianity

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