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We analyzed the performance of a perturbation theory for nonlinearcosmological dynamics, based on the Lagrangian description of hydrodynamics. Inour previous paper, we solved hydrodynamic equations for a self-gravitatingfluid with pressure, given by a polytropic equation of state, using aperturbation method. Then we obtained the first-order solutions in genericbackground universes and the second-order solutions for a wider range ofpolytrope exponents. Using these results, we describe density fields withscale-free spectrum, SCDM, and LCDM models. Then we analyze cross-correlationcoefficient of the density field between N-body simulation and Lagrangianlinear perturbation theory, and the probability distribution of densityfluctuation. From our analyses, for scale-free spectrum models, the case of thepolytrope exponent 5/3 shows better performance than the Zel'dovichapproximation and the truncated Zel'dovich approximation in a quasi-nonlinearregime. On the other hand, for SCDM and LCDM models, improvement by the effectof the velocity dispersion was small.Comment: 23 pages, 9 figures; some figures are replaced; accepted for  publication in Phys.Rev.

Density field in extended Lagrangian perturbation theory