Density field in extended Lagrangian perturbation theory

We analyze the performance of a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. In our previous paper, we solved the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method. Then we obtained the first-order solutions in generic background universes and the second-order solutions for a wider range of polytrope exponents. Using these results, we describe density fields with a scale-free spectrum, SCDM, and LCDM models. Then we analyze the cross-correlation coefficient of the density field between N-body simulation and Lagrangian linear perturbation theory, and the probability distribution of the density fluctuations. From our analyses, for scale-free spectrum models, the case of the polytrope exponent 5/3 shows better performance than the Zel'dovich approximation and the truncated Zel'dovich approximation in the quasinonlinear regime. On the other hand, for SCDM and LCDM models, the improvement by including the effect of the velocity dispersion was small.