Simple estimate of the statistics of large scale structure

We examine the low order moments of inflationary density fluctuations in simple scalar field inflationary models. Using observational constraints on the average amplitude of cosmological density fluctuations we constrain the size of any possible non-Gaussian effects. We find that they are small (with a skewness less than ∼10-6 and a kurtosis less than ∼10-12). We show that these results are consistent with previous work based on a stochastic model for the evolution of the inflaton field distribution.