Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation

TL;DR

This paper extends a diagrammatic Feynman-like approach to calculate n-point correlators of the primordial curvature perturbation, including vector field perturbations, aiming to simplify and popularize the method in cosmology.

Contribution

The work introduces an extended diagrammatic method that incorporates vector field perturbations into the calculation of primordial correlators, facilitating analysis of anisotropic inflation scenarios.

Findings

Developed Feynman-like rules for vector field perturbations

Simplified calculation of anisotropic correlators

Enhanced tools for analyzing statistical anisotropy

Abstract

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation \zeta was developed a few years ago following the spirit of the Feynman rules in Quantum Field Theory. The methodology is very useful and time-saving, as it is for the case of the Feynman rules in the particle physics context, but, unfortunately, is not very well known by the cosmology community. In the present work, we extend such an approach in order to include not only scalar field perturbations as the generators of \zeta, but also vector field perturbations. The purpose is twofold: first, we would like the diagrammatic approach (which we would call the Feynman-like rules) to become widespread among the cosmology community; second, we intend to give an easy tool to formulate any correlator of \zeta for those cases that involve vector field perturbations and that, therefore, may generate prolonged stages of anisotropic expansion and/or important levels of statistical anisotropy. Indeed, the usual way of formulating such correlators, using the Wick's theorem, may become very clutter and time-consuming.