Lecture notes on non-Gaussianity

TL;DR

This paper reviews how primordial non-Gaussianity measurements constrain early universe models, discusses key inflationary models producing non-Gaussianity, and provides tools for calculating related three-point correlations.

Contribution

It offers a comprehensive overview of non-Gaussianity in cosmology, including models, observational constraints, and practical computational methods.

Findings

Observations are consistent with Gaussian initial conditions.

Deviations from Gaussianity are constrained to sub percent levels.

Provides practical tools for calculating three-point correlation functions.

Abstract

We discuss how primordial non-Gaussianity of the curvature perturbation helps to constrain models of the early universe. Observations are consistent with Gaussian initial conditions, compatible with the predictions of the simplest models of inflation. Deviations are constrained to be at the sub percent level, constraining alternative models such as those with multiple fields, non-canonical kinetic terms or breaking the slow-roll conditions. We introduce some of the most important models of inflation which generate non-Gaussian perturbations and provide practical tools on how to calculate the three-point correlation function for a popular class of non-Gaussian models. The current state of the field is summarised and an outlook is given.