Sample Variance of the Higher-Order Cumulants of Cosmic Density and Velocity Fields

Abstract

If primordial fluctuation is Gaussian distributed, higher-order cumulants of the cosmic fields reflect nonlinear mode coupling and provide useful information of gravitational instability picture of structure formation. We show that their expected deviation (sample variance) from the universal values is nonvanishing even in linear theory in the case where observed volume is finite. As a result, we find that the relative sample variance of the skewness of the smoothed velocity divergence field remains as large as $\sim 30%$ even if the survey depth is as deep as $\sim 150h^{1}Mpc$.