We present results showing an improvement of the accuracy of perturbation
theory as applied to cosmological structure formation for a useful range of
quasilinear scales. The Lagrangian theory of gravitational instability of an
Einstein-de Sitter dust cosmogony investigated and solved up to the third order
in the series of papers by Buchert (1989, 1992, 1993a), Buchert \& Ehlers
(1993), Buchert (1993b), Ehlers \& Buchert (1993), is compared with numerical
simulations. In this paper we study the dynamics of pancake models as a first
step. In previous work (Coles \etal 1993, Melott \etal 1993, Melott 1993) the
accuracy of several analytical approximations for the modeling of large-scale
structure in the mildly non-linear regime was analyzed in the same way,
allowing 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 density field in the mildly
non-linear regime (i.e. up to a linear r.m.s. density contrast of σ≈2). The performance of ZA in hierarchical 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 corrections in the displacement mapping from
homogeneity. We study a single pancake model (truncated power-spectrum with
power-index n=−1) using cross-correlation statistics employed inComment: TeX, 18 pages excl.figures; contact [email protected] ;
[email protected] . submitted to Astron. & Astrophy
