Conditions for large non-Gaussianity in two-field slow-roll inflation

Byrnes, Christian T.; Choi, Ki‐Young; Hall, Lisa M.

doi:10.1088/1475-7516/2008/10/008

Cited by 124 publications

(159 citation statements)

References 66 publications

(136 reference statements)

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“…al. [48]. The benefit of our variant of these same conditions is that our version shows that the amplitude of the isocurvature modes at the end of inflation and their sensitivity to perturbations in the classical trajectory are what determines whether non-Gaussianity has any chance of being large.…”

Section: Conditions For Large |Fnl|mentioning

confidence: 92%

“…Here, the approximately 50-fold difference in the total sourcing stems more from the difference in the turn rates for the two trajectories, which both possess large isocurvature modes. Interestingly, the trajectory that rolls along the ridge (solid lines) produces |fNL| ∼ 10 2 , while the neighboring trajectory (dashed lines) corresponds to |fNL| ≈ 1 [48], visually illustrating the role of fine-tuning in achieving large non-Gaussianity.…”

Section: Conditions For Large |Fnl|mentioning

confidence: 99%

“…al. thoroughly investigated in [48]. We set λ = 0.05 and illustrate the results for two trajectories: (1) one that starts at (φ * 1 , φ * 2 ) = (17, 10 −4 ), follows along the ridge, and turns slightly at the end of inflation (solid lines), and (2) a neighboring trajectory that starts only |∆φ * | = 0.01 away in field space, but that eventually rolls off the narrow ridge (dashed lines).…”

Section: Conditions For Large |Fnl|mentioning

confidence: 99%

“…However, if inflation is described by some non-minimal modification, such as multiple fields or higher derivative operators in the inflationary Lagrangian, then non-Gaussianity might be observable in the near future. Indeed, there have been many attempts to calculate the level of non-Gaussianity in general multi-field models (e.g., [31][32][33][34][35][36][37][38][39][40][41][42]), as well as in two-field models (e.g., [43][44][45][46][47][48][49][50][51]). However, it has been very difficult to find models that produce large nonGaussianity, though some exceptions have been found such as in the curvaton model [52][53][54][55][56][57][58], hybrid and multibrid inflation (e.g., [59][60][61][62][63][64][65][66][67]), in certain modulated and tachyonic (p)re-heating scenarios (e.g., [68][69][70][71][72][73][74]), and in some quadratic small-field, two-field models by taking appropriate care of loop correc...…”

Section: Introductionmentioning

confidence: 99%

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Non-Gaussianity in two-field inflation

2011

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We derive semi-analytic formulae for the local bispectrum and trispectrum in general two-field inflation and provide a simple geometric recipe for building observationally allowed models with observable non-Gaussianity. We use the δN formalism to express the bispectrum in terms of spectral observables and the transfer functions, which encode the super-horizon evolution of modes. Similarly, we calculate the trispectrum and show that the trispectrum parameter τNL can be expressed entirely in terms of spectral observables, which provides a new consistency relation unique to two-field inflation. We show that in order to generate observably large non-Gaussianity during inflation, the sourcing of curvature modes by isocurvature modes must be extremely sensitive to a change in the initial conditions orthogonal to the inflaton trajectory and that the amount of sourcing must be non-zero. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories through the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn somewhat in field space. Therefore, it follows that under our assumptions, two-field scenarios with attractor solutions necessarily produce small nonGaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation, and why it has only been achieved in a narrow class of models where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize at least qualitatively to multi-field inflation and to scenarios where the interplay between curvature and isocurvature modes can be represented by the transfer function formalism.

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Section: Conditions For Large |Fnl|mentioning

confidence: 92%

Section: Conditions For Large |Fnl|mentioning

confidence: 99%

Section: Conditions For Large |Fnl|mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Gaussianity in two-field inflation

2011

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“…Whilst Eqs. (22)(23) are equivalent to Eqs. (17)(18), they possess significant computational advantages over the former since they involve lower order δN derivatives which are relatively easier to compute in general compared to higher order ones.…”

Section: The δN Formalismmentioning

confidence: 99%

Influence of reheating on the trispectrum and its scale dependence

Leung¹,

Tarrant²,

Byrnes³

et al. 2013

J. Cosmol. Astropart. Phys.

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We study the evolution of the non-linear curvature perturbation during perturbative reheating, and hence how observables evolve to their final values which we may compare against observations. Our study includes the evolution of the two trispectrum parameters, gNL and τNL, as well as the scale dependence of both fNL and τNL. In general the evolution is significant and must be taken into account, which means that models of multifield inflation cannot be compared to observations without specifying how the subsequent reheating takes place. If the trispectrum is large at the end of inflation, it normally remains large at the end of reheating. In the classes of models we study, it remains very hard to generate τNL f 2 NL , regardless of the decay rates of the fields. Similarly, for the classes of models in which gNL τNL during slow-roll inflation, we find the relation typically remains valid during reheating. Therefore it is possible to observationally test such classes of models without specifying the parameters of reheating, even though the individual observables are sensitive to the details of reheating. It is hard to generate an observably large gNL however. The runnings, n f NL and nτ NL , tend to satisfy a consistency relation nτ NL = (3/2)n f NL regardless of the reheating timescale, but are in general too small to be observed for the class of models considered.

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Lecture Notes on Non-Gaussianity

Byrnes

2016

The Cosmic Microwave Background

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We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the three-point correlation function for a popular class of non-Gaussian models. The current state of the field is summarised and an outlook is given. CONTENTS

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Conditions for large non-Gaussianity in two-field slow-roll inflation

Cited by 124 publications

References 66 publications

Non-Gaussianity in two-field inflation

Non-Gaussianity in two-field inflation

Influence of reheating on the trispectrum and its scale dependence

Lecture Notes on Non-Gaussianity

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