We use cosmological N-body simulations to investigate whether measurements of the moments of large-scale structure can yield constraints on primordial non-Gaussianity .
We measure the variance , skewness , and kurtosis of the evolved density field from simulations with Gaussian and three different non-Gaussian initial conditions : a local model with f _ { \mathrm { NL } } = 100 , an equilateral model with f _ { \mathrm { NL } } = -400 , and an orthogonal model with f _ { \mathrm { NL } } = -400 .
We show that the moments of the dark matter density field differ significantly between Gaussian and non-Gaussian models .
We also make the measurements on mock galaxy catalogs that contain galaxies with clustering properties similar to those of luminous red galaxies ( LRGs ) .
We find that , in the case of skewness and kurtosis , galaxy bias reduces the detectability of non-Gaussianity , though we can still clearly discriminate between different models in our simulation volume .
However , in the case of the variance , galaxy bias greatly amplifies the detectability of non-Gaussianity .
In all cases we find that redshift distortions do not significantly affect the detectability .
When we restrict our measurements to volumes equivalent to the Sloan Digital Sky Survey II ( SDSS-II ) or Baryon Oscillation Spectroscopic Survey ( BOSS ) samples , the probability of detecting a departure from the Gaussian model is high by using measurements of the variance , but very low by using only skewness and kurtosis measurements .
For example , if our local non-Gaussian model were the true model in the universe , a variance measurement in the BOSS survey would have a \sim 95 % chance of detecting this non-Gaussiantity at the 2 \sigma level , whereas a skewness measurement would only have at best a \sim 25 % chance of doing so .
We estimate that in order to detect an amount of non-Gaussianity that is consistent with recent CMB constraints using skewness or kurtosis , we would need a galaxy survey that is much larger than any planned future survey .
Skewness and kurtosis measurements are thus never likely to yield useful constraints on primordial non-Gaussianity .
On the other hand , future surveys should be large enough to place meaningful constraints using measurements of the galaxy variance .