Understanding non-Gaussianity signatures in general relativity

Possible departure from Gaussian statistics in cosmological perturbations can shed much light on the physics of their generation in the primordial Universe. Many of the forthcoming surveys of the large-scale structure with unprecedented survey volume aim at detecting these signatures. However, ignoring the ``gauge artifacts'' in general relativity that arise from the freedom to choose arbitrary space-time coordinates to describe the perturbed Universe can lead to incorrect interpretation on the observational consequences of these non-Gaussian signatures. I present two important examples of non-Gaussianity signatures. I show that in the ``separate universes'' formalism it can be clarified that they are strictly forbidden in canonical inflation scenarios involving only one scalar degree of freedom. One is a quadrupolar direction-dependence in the power spectrum of matter density, which is naively expected from a non-Gaussian correlation between a primordial gravitational wave of super-horizon wavelength and two density perturbations of shorter wavelengths. The other is a galaxy biasing that grows toward large scales, which is naively expected from nonlinearity in general relativity that couples a long-wavelength gravitational potential with two short-wavelength density fluctuations. Conversely, general models of single-field inflation can be falsified if it turns out that either of those signatures is actually observed.