The real shape of non-Gaussianities
  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.
