Diagrammatic approach to non-Gaussianity from inflation

We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter fNL in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity even during slow-roll inflation with Gaussian perturbations at Hubble exit. In this paper we give the general conditions to obtain large non-Gaussianity and calculate the level of fine-tuning required to obtain this. We present explicit models in which the non-Gaussianity at the end of inflation can exceed the current observational bound of |fNL| 100.

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“…[42]. However they can still be significant if the coefficient to the term given by the derivative of N is extremely large, e.g.…”

Section: Hybrid Inflationmentioning

confidence: 99%

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

Byrnes

Choi

Hall

2008

J. Cosmol. Astropart. Phys.

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“…This method is based on the diagrammatic approach given in Ref. [9] as well as on our previous work [10,11], in which the formulation for the bi-spectrum was developed. As for the parameterization of the higher order spectra, it is well known that the bi-spectrum can be parameterized by a single parameter, so-called non-linearity parameter, f N L , while the tri-spectrum is parameterized by two parameters τ N L and g N L [12] due to the existence of two distinct terms that exhibit a different wavenumber dependence.…”

Section: Introductionmentioning

confidence: 99%

Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations

Yokoyama

Suyama²,

Tanaka

2009

J. Cosmol. Astropart. Phys.

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We present a new efficient method for computing the non-linearity parameters of the higher order correlation functions of local type curvature perturbations in inflation models having a N -component scalar field, focusing on the non-Gaussianity generated during the evolution on super-horizon scales. In contrast to the naive expectation that the number of operations necessary to compute the npoint functions is proportional to N n , it grows only linearly in N in our formalism. Hence, our formalism is particularly powerful for the inflation models composed of a multi-component scalar field, including the models in which the slow-roll conditions are violated after the horizon crossing time. Explicit formulas obtained by applying our method are provided for n = 2, 3, 4 and 5, which correspond to power-, bi-, tri-and quad-spectra, respectively. We also discuss how many parameters we need to parameterize the amplitude and the shape of the higher order correlation functions of local type.

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“…those involving multiple fields, the curvature perturbation ζ is not constant after horizon exit. Therefore evolution after horizon exit might lead to non-Gaussian effects, which has been investigated in [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. These investigations have been done by solving classical equations of motion, which is assumed to be a good approximation to the quantum theory, because quantum effects are presumably negligible for wavelengths much longer than the horizon length (see [28] for a recent argument).…”

Section: Introductionmentioning

confidence: 99%

Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

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Abstract:We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study φ 3 theory on a de Sitter background for a massless minimally coupled scalar field φ. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale H are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.

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Diagrammatic approach to non-Gaussianity from inflation

Cited by 73 publications

References 62 publications

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

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

Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations

Classical approximation to quantum cosmological correlations

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