The real shape of non-Gaussianities

TL;DR

This paper explores the real-space shapes and physical implications of various non-Gaussianities, including bispectra and trispectra, in cosmology, highlighting their geometric forms, origins, and observational signatures.

Contribution

It provides a detailed real-space interpretation of non-Gaussian shapes, including bispectra and trispectra, and discusses their physical origins and observational consequences.

Findings

Equilateral bispectrum corresponds to concentrated overdensities and filaments.

Flattened shapes relate to line-like structures such as cosmic strings.

Squeezed trispectra reveal correlations between large-scale and small-scale fluctuations.

Abstract

I review what bispectra and trispectra look like in real space, in terms of the sign of particular shaped triangles and tetrahedrons. Having an equilateral density bispectrum of positive sign corresponds to having concentrated overdensities surrounded by larger weaker underdensities. In 3D these are concentrated density filaments, as expected in large-scale structure. As the shape changes from equilateral to flattened the concentrated overdensities flatten into lines (3D planes). I then focus on squeezed bispectra, which can be thought of as correlations of changes in small-scale power with large-scale fields, and discuss the general non-perturbative form of the squeezed bispectrum and its angular dependence. A general trispectrum has tetrahedral form and I show examples of what this can look like in real space. Squeezed trispectra are of particular interest and come in two forms, corresponding to large-scale variance of small-scale power, and correlated modulations of an equilateral-form bispectrum. Flattened trispectra can be produced by line-like features in 2D, for example from cosmic strings, and randomly located features also give a non-Gaussian signal. There are relationships between the squeezed types of non-Gaussianity, and also a useful interpretation in terms of statistical anisotropy. I discuss the various possible physical origins of cosmological non-Gaussianities, both in terms of primordial perturbations and late-time dynamical and geometric effects.