Revisiting non-Gaussianity from non-attractor inflation models

Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

doi:10.1088/1475-7516/2018/05/012

Cited by 114 publications

(177 citation statements)

References 64 publications

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“…This numerical result can be understood from Ref. [37]'s analytic study of infinitely sharp potential transitions between USR and SR, which we review briefly in §IV B. Transitions where the inflaton velocity monotonically decreases to reach an attractor solution lead to squeezed non-Gaussianity that is proportional to the potential slow-roll parameters on the attractor. Conversely, transitions where the inflaton instantly goes from having too much kinetic energy for the potential it evolves on to suddenly having insufficient kinetic energy for a now much steeper potential conserve the USR non-Gaussianity.…”

Section: Transient Ultra-slow Rollmentioning

confidence: 79%

“…In §IV C, we generalize the analysis of Ref. [37] to potentials which do not have an infinitely sharp break, and in particular we study how quickly the inflaton must traverse the potential feature to reproduce the USR result. We show that to conserve the USR result Eq.…”

Section: Transient Ultra-slow Rollmentioning

confidence: 99%

“…To understand why the local power spectrum is not enhanced in the inflection-point model and to study generally the non-Gaussianity in transient USR, we first review in §IV B the analytic results of Ref. [37] for infinitely sharp potential transitions from USR to SR. We then generalize that study in §IV C to different types of transitions from USR with the help of an adjustable toy model.…”

Section: Introductionmentioning

confidence: 99%

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Primordial black holes and local non-Gaussianity in canonical inflation

2019

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Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long-and short-wavelength curvature modes, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficient PBHs. Moreover, the transition out of USR, which is necessary for a successful model, suppresses even this small enhancement unless it causes a large increase in the inflaton kinetic energy in a fraction of an e-fold, which we call a large and fast transition. Along the way we apply the in-in formalism, the δN formalism, and gauge transformations to compute non-Gaussianities and illuminate different aspects of the physical origin of these results. Local non-Gaussianity in the squeezed limit does not weaken the Gaussian conclusion that PBHs as dark matter in canonical single-field inflation require a complicated and fine-tuned potential shape with an epoch where slow roll is transiently violated.

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Section: Transient Ultra-slow Rollmentioning

confidence: 79%

Section: Transient Ultra-slow Rollmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Primordial black holes and local non-Gaussianity in canonical inflation

2019

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“…In single-field models of inflation the parameter f NL can be calculated, and it is given by [20,22] f NL = 5 12 −3 + 9 − 12η (1.2)…”

Section: Introductionmentioning

confidence: 99%

Primordial black hole formation with non-Gaussian curvature perturbations

Atal¹,

Garriga²,

Marcos-Caballero³

2019

J. Cosmol. Astropart. Phys.

110

109

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In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude ζ * , corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which ζ * is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.1 A notable exception, where no amplification of the power spectrum is needed, are models where PBH are formed from the collapse of domain walls created during inflation [7,8].2 The amplitude of non-Gaussianities in transient periods of CR is different from their amplitude in a pure CR [16][17][18]. The difference between both scenarios is that in the former the curvature perturbations eventually freeze.

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“…Ultra-slow-roll inflation [11] is a single-field model, where the scalar field is minimally coupled to the metric, and is one of the few examples that violate the standard consistency relations as the curvature in unitary gauge is not conserved for super-horizon modes [21][22][23][24][25][26]. This model has regained attention lately where it has been considered as a transient phase to generate large non-gaussianities and possibly primordial black holes [27][28][29]. Explicitly, USR is a canonical scalar field model with:…”

Section: A Ultra Slow Rollmentioning

confidence: 99%

Curvature perturbations in the effective field theory of inflation

Lagos

Lin

2019

Phys. Rev. D

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We discuss the difference between various gauge-invariant quantities typically used in single-field inflation, namely synchronous ζ s , comoving ζ c , and unitary ζ u curvatures. We show that conservation of ζ c outside the horizon is quite restrictive on models as it leads to conservation of ζ s and ζ u , whereas the reverse does not hold. We illustrate the consequence of these differences with two inflationary models: ultra-slow-roll (USR) and braiding-ultra-slow-roll (BUSR). In USR, we show that out of the three curvatures, only ζ s is conserved outside the horizon, and we connect this result to the concepts of separate universe and the usage of the δ N formalism. We find that even though ζ s is conserved, there is still a mild violation of the separate universe approximation in the continuity equation. Nevertheless, the δ N formalism can still be applied to calculate the primordial power spectrum of some gauge-invariant quantities such as ζ u , although it breaks down for others such as the uniform-density curvature. In BUSR, we show that both ζ u and ζ s are conserved outside the horizon, but take different values. Additionally, since ζ u = ζ c we find that the prediction for observable curvature fluctuations after inflation does not reflect ζ c at horizon crossing during inflation and moreover involves not just ζ u at that epoch but also the manner in which the braiding phase ends.

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Revisiting non-Gaussianity from non-attractor inflation models

Cited by 114 publications

References 64 publications

Primordial black holes and local non-Gaussianity in canonical inflation

Primordial black holes and local non-Gaussianity in canonical inflation

Primordial black hole formation with non-Gaussian curvature perturbations

Curvature perturbations in the effective field theory of inflation

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