The Cosmic Web from Perturbation Theory

TL;DR

This paper develops an extended Lagrangian perturbation theory, called eALPT, incorporating viscosity and vorticity, to accurately model cosmic structure formation at the field level, matching N-body simulations with high precision.

Contribution

It introduces eALPT, an Eulerian extension of LPT with regularisation and vorticity, providing a fast, theoretically grounded model for large-scale structure analysis.

Findings

Cross-correlation with N-body increases to ~95% at k=1 h/Mpc and z=0.

Power spectra match N-body results up to k ≈ 0.3 h/Mpc.

eALPT outperforms Zel'dovich and ALPT approximations.

Abstract

Context: Analyzing the large-scale structure (LSS) with galaxy surveys demands accurate structure formation models. Such models should ideally be fast and have a clear theoretical framework to rapidly scan a variety of cosmological parameter spaces without requiring large training data sets. Aims: This study aims to extend Lagrangian perturbation theory (LPT), including viscosity and vorticity, to reproduce the cosmic evolution from dark matter N-body calculations at the field level. Methods: We extend LPT to an Eulerian framework, which we dub eALPT. An ultraviolet regularisation through the spherical collapse model provided by Augmented LPT, turns out to be crucial at low redshifts. This iterative method enables modelling of the stress tensor and introduces vorticity. The eALPT model has two free parameters apart from the choice of cosmology, redshift snapshots, cosmic volume, and the number of particles. Results: We find that compared to N-body solvers, the cross-correlation of the dark matter distribution increases at $k = 1\,h$ Mpc$^{-1}$ and $z = 0$ from $\sim$55% with the Zel'dovich approximation ($\sim$70% with ALPT), to $\sim$95% with three timesteps eALPT, and the power spectra show percentage accuracy up to $k \simeq 0.3\,h$ Mpc$^{-1}$.