Weakly Nonlinear Clustering for Arbitrary Expansion Histories

Abstract

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.