A bound concerning primordial non-Gaussianity

103

We present Feynman type diagrams for calculating the n-point function of the primordial curvature perturbation in terms of scalar field perturbations during inflation. The diagrams can be used to evaluate the corresponding terms in the n-point function at tree level or any required loop level. Rules are presented for drawing the diagrams and writing down the corresponding terms in real space and Fourier space. We show that vertices can be renormalised to automatically account for diagrams with dressed vertices. We apply these rules to calculate the primordial power spectrum up to two loops, the bispectrum including loop corrections, and the trispectrum.

Section: A Power Spectrummentioning

confidence: 96%

Diagrammatic approach to non-Gaussianity from inflation

Byrnes

Koyama

Sasaki

et al. 2007

103

“…They are specified respectively by [15] quantities f NL and τ NL . Taking the field perturbations to be perfectly gaussian, which has been justified for the bispectrum [83,84], and ignoring the scale-dependence of the spectra, the predictions are [77,85] 16 10) where A and B are of order 1 on cosmological scales. Present observation [87] gives roughly |f NL | 100, and absent a detection the eventual bound will be [88] |f NL | 1.…”

Section: Multi-component Chaotic Inflationmentioning

confidence: 99%

Inflation models and observation

Alabidi

Lyth

2006

Self Cite

184

281

We consider small-field models which invoke the usual framework for the effective field theory, and large-field models which go beyond that. Present and future possibilities for discriminating between the models are assessed, on the assumption that the primordial curvature perturbation is generated during inflation. With PLANCK data, the theoretical and observational uncertainties on the spectral index will be comparable, providing useful discrimination between small-field models.Further discrimination between models may come later through the tensor fraction, the running of the spectral index and non-gaussianity. The prediction for the trispectrum in a generic multi-field inflation model is given for the first time.

“…In the long-term, it may be possible to obtain even better estimates from observations, perhaps based on maps of the 21-cm emission of neutral hydrogen [19,20]. On the theoretical side, predictions for the non-gaussianity generated in a large collection of relevant models have become available over the last several years [21,22,10,23,24,25,26,27,28,29,30,8,31,32,33], following Maldacena's successful calculation of the bispectrum produced in single-field, slow-roll inflation [34].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussianity of inflationary field perturbations from the field equation

Seery¹,

Malik²,

Lyth³

2008

Self Cite

Abstract. We calculate the tree-level bispectrum of the inflaton field perturbation directly from the field equations, and construct the corresponding f NL parameter. Our results agree with previous ones derived from the Lagrangian. We argue that quantum theory should only be used to calculate the correlators when they first become classical a few Hubble times after horizon exit, the classical evolution taking over thereafter.