Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory

TL;DR

This paper introduces a fast, efficient method called ALPT that combines second order LPT and spherical collapse to improve modeling of cosmic structure formation across all scales, outperforming previous approximations.

Contribution

The paper presents a novel combined ALPT approach that integrates 2LPT and spherical collapse, significantly enhancing accuracy in modeling structure formation compared to existing methods.

Findings

ALPT shows ~25% higher correlation than 2LPT at k=1 h Mpc^-1.

ALPT shows ~75% higher correlation than 2LPT at k=2 h Mpc^-1.

Optimal smoothing radius for maximum correlation is 4-5 h^-1 Mpc.

Abstract

We present a new fast and efficient approach to model structure formation with Augmented Lagrangian Perturbation Theory (ALPT). Our method is based on splitting the displacement field into a long and a short-range component. The long-range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the result of 25 dark matter only N-body simulations to benchmark at z=0 the different approximations: 1st, 2nd, 3rd order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing ~25% and ~75% higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc^-1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with r_S = 4 - 5 h^-1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.