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

Abstract

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 $\mathcal{N}$-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 $n$-point functions is proportional to ${\mathcal{N}}^n$, it grows only linearly in $\mathcal{N}$ in our formalism. Hence, our formalism is particularly powerful for the inflation models composed of a multi-component scalar field. Explicit formulas obtained by applying our method are provided for $n=2,3,4$ and 5, which correspond to power-, bi-, tri- and {\it 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.

17 pages, 11 figures, 2 tables, minor revisions

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Cited by in corpus (21)

• On Classification of Models of Large Local-Type Non-Gaussianity
• Inflationary perturbation theory is geometrical optics in phase space
• Observational imprints of enhanced scalar power on small scales in ultra slow roll inflation and associated non-Gaussianities
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum
• Transport equations for the inflationary trispectrum
• The δN formula is the dynamical renormalization group
• The squeezed limit of the bispectrum in multi-field inflation
• Transporting non-Gaussianity from sub to super-horizon scales
• Inhomogeneous non-Gaussianity
• The hemispherical asymmetry from a scale-dependent inflationary bispectrum
• Inflation in Multi-field Modified DBM Potentials
• Predictions in multifield models of inflation
• Testing supersymmetric Higgs inflation with non-Gaussianity
• The Separate Universe Approach to Soft Limits
• Cosmological observables in multi-field inflation with a non-flat field space
• On Non-Gaussianities in Two-Field Poly-Instanton Inflation
• Statistics of general functions of a Gaussian field -application to non-Gaussianity from preheating-
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Quadra-Spectrum and Quint-Spectrum from Inflation and Curvaton Models
• Extension of local-type inequality for the higher order correlation functions
• Local Scale-Dependent Non-Gaussian Curvature Perturbations at Cubic Order