# The real shape of non-Gaussianities

## 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. I discuss the various possible physical origins of these non-Gaussianities, both in terms of primordial perturbations and late-time dynamical and geometric effects, and the relationship with statistical anisotropy.

- Authors:

- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22280236

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2011; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; ASTROPHYSICS; CORRELATIONS; COSMOLOGY; DENSITY; DISTURBANCES; MODULATION; SPACE; STRING MODELS

### Citation Formats

```
Lewis, Antony, E-mail: antony@cosmologist.info.
```*The real shape of non-Gaussianities*. United States: N. p., 2011.
Web. doi:10.1088/1475-7516/2011/10/026.

```
Lewis, Antony, E-mail: antony@cosmologist.info.
```*The real shape of non-Gaussianities*. United States. doi:10.1088/1475-7516/2011/10/026.

```
Lewis, Antony, E-mail: antony@cosmologist.info. Sat .
"The real shape of non-Gaussianities". United States. doi:10.1088/1475-7516/2011/10/026.
```

```
@article{osti_22280236,
```

title = {The real shape of non-Gaussianities},

author = {Lewis, Antony, E-mail: antony@cosmologist.info},

abstractNote = {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. I discuss the various possible physical origins of these non-Gaussianities, both in terms of primordial perturbations and late-time dynamical and geometric effects, and the relationship with statistical anisotropy.},

doi = {10.1088/1475-7516/2011/10/026},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 10,

volume = 2011,

place = {United States},

year = {2011},

month = {10}

}