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

Abstract

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation ζwas 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 ζ, 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 ζfor 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.

LaTeX file, 26 pages. v2: A short discussion added regarding the role of the diagrams in high precision cosmology as well as in those cases where the loop contributions are larger than the tree level terms, generating large and observable levels of (anisotropic) non-gaussianity; references added, conclusions unchanged. v3: version to appear in Journal of Cosmology and Astroparticle Physics