Skewness and large-scale structure

The evolution of the skewness, γ, of the cosmological mass distribution into the nonlinear regime is discussed. Various analytical estimates of the skewness of initially Gaussian (i.e. unskewed) density perturbations are compared with each other, with N-body results and with real clustering data. We find that, in general, the skewness is simply related to the rms mass fluctuation on the scale in question: $$\gamma = A {\sigma }^{4}\enspace \text {where}\enspace A\simeq 3$$ is a constant. This relationship can be used to construct a simple but potentially powerful test of the hypothesis that large-scale structure in the Universe evolved from Gaussian initial conditions. In particular, we find that the measured skewness of the QDOT redshift survey density distribution is compatible with the gravitational evolution of sufficiently high-amplitude Gaussian fluctuations. There is therefore no need to invoke non-Gaussian initial fluctuations to explain these data. We also discuss in detail the role of discreteness (i.e. shot noise) effects upon the interpretation of cell-count statistics.