TEMPORAL OPTIMIZATION OF LAGRANGIAN PERTURBATION SCHEMES

The Lagrangian perturbation theory on Friedmann-Lemaitre cosmologies i s compared with numerical simulations (tree-, adaptive (PM)-M-3- and P M codes). In previous work we have probed the large-scale performance of the Lagrangian perturbation solutions up to the third order by stud ying their cross-correlations with N-body simulations for various powe r spectra (Buchert et al. 1994, Melott et al. 1995, Weiss et al. 1996) . Thereby, spatial optimization techniques were applied by (high-frequ ency-)filtering of the initial power spectra. In this work the novel m ethod of temporal optimization [Shifted-Time-Approximation (STA) and F rozen-Time-Approximation (FTA)] is investigated and used. The method i s designed to compensate the native property of Lagrangian perturbatio n solutions to delay the collapse of structures. The method can be tre ated analytically. Applying the STA and FTA prescriptions a significan t improvement of the performance of Lagrangian perturbation schemes up to r.m.s density contrast of about 10 (as measured by cross-correlati on, relative phase error and power-spectrum statistics) is observed. U sing this tool we investigate a local study of special clustering mode ls of dark matter as candidates for typical elements of the large-scal e structure in the Universe, and so also focus on the performance of t he perturbation solutions on smaller scales at high-spatial resolution . The models analyzed were presented in (Buchert et al. 1997) and allo w studying typical features of the clustering process in the non-linea r regime. The spatial and temporal limits of applicability of the solu tions at second and third order are determined and compared with the f irst-order solution, which is equivalent to the ''Zel'dovich approxima tion'' (Zel'dovich 1970, 1973) for the type of initial data analyzed.