TESTING TREE-LEVEL PERTURBATION-THEORY FOR LARGE-SCALE STRUCTURE WITHTHE LOCAL LAGRANGIAN APPROXIMATION

We test tree-level perturbation theory for Gaussian initial conditions with power spectra P(k)proportional to k(n) by comparing the probabil ity distribution function (PDF) for the density predicted by the local Lagrangian approximation (LLA) with the results of numerical gravitat ional clustering simulations. Our results indicate that our approximat ion correctly reproduces the evolved density PDF for n = -1 and -2 pow er spectra up to the weakly non-linear regime, while it shows marginal agreement for power indices n = 0 and +1 in the linear regime and poo r agreement beyond this point. This suggests that tree-level perturbat ion theory (as realized in the LLA) can accurately predict the density distribution function for n less than or equal to -1, but fails for n greater than or equal to 0.