Weakly Nonlinear Clustering for Arbitrary Expansion Histories

Bouchet et al. (1992) showed that in an open or closed Universe with only pressureless matter, gravitational instability from Gaussian initial conditions induces a normalized skewness, S3 ≡ 〈δ 〉 〈δ〉 −2 , that has only a very weak dependence on the nonrelativistic-matter density. Here we generalize this result to a plethora of models with various contributions to the total energy density, including nonrelativistic matter, a cosmological constant, and other forms of missing energy. Our numerical results show that the skewness (and bispectrum) depend only very weakly (∼< 2%) on the expansion history. Thus, the skewness and bispectrum provide a robust test of gravitational instability from Gaussian initial conditions, independent of the underlying cosmological model. Subject headings: cosmology: theory — galaxies: large scale structure of the universe — galaxies: clustering — galaxies: statistics