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

TL;DR

GridSPT introduces a fast, grid-based perturbation theory algorithm for large-scale structure analysis, accurately reproducing N-body simulation results on large scales using FFT, and offering a new tool for cosmological studies.

Contribution

The paper presents a novel grid-based algorithm for standard perturbation theory that efficiently computes higher-order density fields from linear spectra.

Findings

GridSPT accurately reproduces N-body results on large scales.

The method is computationally efficient using FFT.

Performance decreases for smaller smoothing scales and under-dense regions.

Abstract

Perturbation theory (PT) calculation of large-scale structure has been used to interpret the observed non-linear statistics of large-scale structure at the quasi-linear 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 structure. 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 non-linear 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 under-dense regions where we find that 2LPT (second-order Lagrangian perturbation theory) algorithm performs well.