Modelling the matter bispectrum towards nonlinear scales - two and three loops in perturbation theories

TL;DR

This paper advances the modeling of the matter bispectrum in large-scale structure by computing two- and three-loop corrections in perturbation theories, improving accuracy at nonlinear scales and comparing results with numerical simulations.

Contribution

It provides the first detailed computation of the matter bispectrum up to two and three loops in different perturbation theories, including infrared-safe integrands and comparison with simulations.

Findings

Two-loop Standard Perturbation Theory improves accuracy up to certain scales.

Three-loop MPTbreeze extends modeling to smaller scales.

Results show better agreement with simulations at higher loop orders.

Abstract

I compute the matter bispectrum of large-scale structure up to two loops in the Standard Perturbation Theory and up to three loops in the MPTbreeze renormalised perturbation theory, determining the contributing loop diagrams and evaluating them numerically. In the process I remove the leading divergences in the integrands, thus making them infrared-safe. By comparing the results to numerical simulations, I show that in the case of the Standard Perturbation Theory, the bispectrum at two loops is more accurate than at one loop, up to $k_{\textrm{max}} \sim 0.09 \, h/\textrm{Mpc}$ at $z=0$ and $k_{\textrm{max}} \sim 0.11 \, h/\textrm{Mpc}$ at $z=1$. The MPTbreeze can be employed to accurately model the matter bispectrum up to $k_{\textrm{max}} \sim 0.17 \, h/\textrm{Mpc}$ at $z=0$ and $k_{\textrm{max}} \sim 0.24 \, h/\textrm{Mpc}$ at $z=1$ using the results at three loops.