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, SCDM (standard cold dark matter) and BSI (broken scale invariance). The latter model we study 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 so obtained Lagrangian mappings are computed for a set of COBE-normalized SCDM and BSI initial data of different sizes and at different times. We compare these results against those obtained with a numerical 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 nonlinearities in the model can produce more small-scale power, if initially such power is removed. The optimization scheme can be expressed in a way which is independent of the type of fluctuation spectrum and of the size of the simulations. (orig.)