Optimizing higher order Lagrangian perturbation theory for standard CDM and BSI models

We investigate the performance of Lagrangian perturbation theory up to the second order for two scenarios of cosmological large-scale structure formation, standard cold dark matter (SCDM) and broken scale invariance (BSI). We study the latter model as a representative of COBE-normalized CDM models which fit the small-scale power of galaxy surveys. In this context, we optimize the performance of the Lagrangian perturbation schemes by smoothing the small-scale fluctuations in the initial data. The results of the Lagrangian mappings obtained are computed for a set of COBE-normalized SCDM and BSI initial data of different sizes and at different times. We compare these results with those obtained with a numerical particle mesh (PM) code. We find an excellent performance of the optimized Lagrangian schemes down to scales close to the correlation length. This is explained by the counterintuitive fact that non-linearities in the model can produce more small-scale power, if initially such power is removed. The optimization schemes can be expressed in a way that is independent of the type of fluctuation spectrum and the size of the simulations.