TESTING HIGHER-ORDER LAGRANGIAN PERTURBATION-THEORY AGAINST NUMERICALSIMULATIONS .1. PANCAKE MODELS

We present results showing an improvement of the accuracy of perturbat ion theory as applied to cosmological structure formation for a useful range of quasilinear scales. The Lagrangian theory of gravitational i nstability of an Einstein-de Sitter dust cosmogony investigated and so lved up to the third order in the series of papers by Buchert (1989, 1 992, 1993), Buchert & Ehlers (1993), Buchert (1994), Ehlers & Buchert (1994), is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work (Col es et al. 1993; Melott et al. 1994a; Melott 1993) the accuracy of seve ral analytical approximations for the modeling of large-scale structur e in the mildly non-linear regime was analyzed in the same way, allowi ng for direct comparison of the accuracy of various approximations. In particular, the ''Zel'dovich approximation'' (Zel'dovich 1970, 1973, hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the dens ity field in the mildly non-linear regime (i.e. up to a linear rms den sity contrast of sigma almost-equal-to 2). The performance of ZA in hi erarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order c orrections in the displacement mapping from homogeneity. We study a si ngle pancake model (truncated power-spectrum with power-index n = - 1) using cross-correlation statistics employed in previous work. We foun d that for all statistical methods used the higher-order corrections i mprove the results obtained for the first-order solution up to the sta ge when sigma(linear theory) almost-equal-to 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, thi rd-order is not much improvement over second-order at any stage. The t otal breakdown of the perturbation approach is observed at the stage, where sigma(linear theory) almost-equal-to 2, which corresponds to the onset of hierarchical clustering. This success is found at a consider ably higher non-linearity than is usual for perturbation theory. Wheth er a truncation of the initial power-spectrum in hierarchical models r etains this improvement will be analyzed in a forthcoming work.