Lagrangian perturbations theory : Third-order solution for general dark energy models

Abstract

We investigate the Lagrangian perturbation theory of a general dark energy models with a constant equation of state, ω, and derive the fitting form of the fastest growing mode solutions up to the third order. These fitting forms are less than few % errors compared to the numerical calculation. We also correct the solutions of Einstein-de Sitter and the open universe with the proper initial conditions and the correct consideration for the growing mode solutions in order to compare with the general dark energy models. Even though these fitting forms are limited to the constant equation of state models, one can apply these to the time-varying ωby interpolating between models with the constant ω. These fitting forms can be used for the correct prediction for the two point correlation function and can give the proper predictions for the different dark energy models.