Testing tree-level perturbation theory for large-scale structure with the local Lagrangian approximation

We test tree-level perturbation theory for Gaussian initial conditions withpower spectra $P(k)\propto k^n$ by comparing the probability distributionfunction (PDF) for the density predicted by the Local Lagrangian Approximation(LLA) with the results of numerical gravitational clustering simulations. Ourresults indicate that our approximation correctly reproduces the evolveddensity PDF for $-3 \leq n \leq-1$ power spectra up to the weakly nonlinearregime, while it shows marginal agreement for power indices n=0 and +1 in thelinear regime and poor agreement beyond this point. This suggests thattree-level perturbation theory (as realized in the Local LagrangianApproximation) can accurately predict the density distribution function for $-3\leq n \leq -1$ but fails for $n \ge 0$.Comment: 10 pages, latex, 2 figure