Diagrammatic approach to non-Gaussianity from inflation

TL;DR

This paper introduces a diagrammatic method for calculating non-Gaussian features of primordial curvature perturbations during inflation, enabling systematic evaluation of n-point functions including loop corrections.

Contribution

It develops Feynman-like diagrams and rules for inflationary perturbations, allowing automatic renormalization and calculation of higher-order correlation functions.

Findings

Calculated the primordial power spectrum up to two loops.

Evaluated the bispectrum with loop corrections.

Analyzed the trispectrum with loop contributions.

Abstract

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.