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, $S_3 \equiv \VEV{\delta^3} \VEV{\delta^2}^{-2}$, 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 ($\lesssim 2$) 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.