Grid-based calculation for perturbation theory of large-scale structure

Perturbation theory calculation of large-scale structures has been used to interpret the observed nonlinear statistics of large-scale structures at the quasilinear regime. In particular, the so-called standard perturbation theory (SPT) provides a basis for the analytical computation of the higher-order quantities of large-scale structures. Here, we present a novel grid-based algorithm for the SPT calculation, hence named GridSPT, to generate the higher-order density and velocity fields from a given linear power spectrum. Taking advantage of the fast Fourier transform, the GridSPT quickly generates the nonlinear density fields at each order, from which we calculate the statistical quantities such as nonlinear power spectrum and bispectrum. Comparing the density fields (to fifth order) from GridSPT with those from the full N-body simulations in the configuration space, we find that GridSPT accurately reproduces the N-body result on large scales. The agreement worsens with smaller smoothing radius, particularly for the underdense regions where we find that the second-order Lagrangian perturbation theory algorithm performs well.