Weakly Nonlinear Clustering for Arbitrary Expansion Histories

Bouchet et al. showed that in an open or closed universe with only pressureless matter, gravitational instability from Gaussian initial conditions induces a normalized skewness, S3≡⟨δ3⟩⟨δ2⟩−2, which 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.