Lagrangian perturbations and the matter bispectrum II: the resummed one-loop correction to the matter bispectrum

TL;DR

This paper advances the understanding of the matter bispectrum in large-scale structure by computing a resummed one-loop correction using Lagrangian perturbation theory, aligning well with N-body simulations and extending to redshift space.

Contribution

It introduces a resummation technique within LPT for the one-loop matter bispectrum, improving theoretical predictions and their agreement with simulations.

Findings

Resummed one-loop bispectrum matches N-body simulations.

LPT and SPT one-loop bispectra are equivalent in the initial position limit.

Method extended to redshift-space bispectrum calculations.

Abstract

This is part two in a series of papers in which we investigate an approach based on Lagrangian perturbation theory (LPT) to study the non-linear evolution of the large-scale structure distribution in the universe. Firstly, we compute the matter bispectrum in real space using LPT up one-loop order, for both Gaussian and non-Gaussian initial conditions. In the initial position limit, we find that the one-loop bispectrum computed in this manner is identical to its counterpart obtained from standard Eulerian perturbation theory (SPT). Furthermore, the LPT formalism allows for a simple reorganisation of the perturbative series corresponding to the resummation of an infinite series of perturbations in SPT. Applying this method, we find a resummed one-loop bispectrum that compares favourably with results from N-body simulations. We generalise the resummation method also to the computation of the redshift-space bispectrum up to one loop.