Non-Gaussianity in large-scale structure and Minkowski functionals

Minkowski functionals (MFs) are topological statistics that have become one of many standard tools used for investigating the statistical properties of cosmological random fields. They have found regular use in studies of departures from Gaussianity in a number of important cosmological scenarios. Important examples include the cosmic microwave background (CMB), weak lensing studies, 21-cm surveys and large-scale structure (LSS). To the lowest order the MFs depend on three generalized skewness parameters that can be shown to probe the bispectrum with differing weights. Recent studies have advocated the use of a power spectrum associated with the bispectrum, called the skew-spectrum, that has more power to distinguish between various contributions to the bispectrum than the conventional formalism adopted when using the MFs. In this article, we review the motivations for studying non-Gaussianity and emphasize the importance of the momentum dependence of higher order correlators in investigating both inflationary and early Universe models as well as analytical models for gravitational instability. We then introduce the skew-spectra, applied to galaxy surveys, as a tool for investigating various models for primordial and gravitationally induced non-Gaussianities. We present analytical expressions for the skew-spectra for the density field and divergence of the velocity field in three dimensions and for projected surveys as a function of redshift and a smoothing angular scale. A Gaussian window function is assumed throughout this paper. Analytical results are derived for the case of gravitationally induced non-Gaussianity. These results can be generalized to incorporate redshift-space effects. This will be useful in probing primordial and gravitationally induced non-Gaussianity from ongoing and future galaxy surveys.