The two and three-loop matter bispectrum in perturbation theories

TL;DR

This paper computes the dark matter bispectrum at two and three loops using perturbation theories, extending the modeling into quasi-nonlinear scales and assessing accuracy improvements.

Contribution

First evaluation of the matter bispectrum at two and three loops in perturbation theories, demonstrating extended modeling capabilities and accuracy limits.

Findings

Standard Perturbation Theory models bispectrum up to $k_{max} \\sim 0.1 \, h/\\text{Mpc}$ at $z=0$

MPTbreeze bispectrum remains accurate up to $k_{max} \\sim 0.17 \, h/\\text{Mpc}$ at $z=0$

Three-loop MPTbreeze improves bispectrum predictions at smaller scales.

Abstract

We evaluate for the first time the dark matter bispectrum of large-scale structure at two loops in the Standard Perturbation Theory and at three loops in the Renormalised Perturbation Theory (MPTbreeze formalism), removing in each case the leading divergences in the integrals in order to make them infrared-safe. We show that the Standard Perturbation Theory at two loops can be employed to model the matter bispectrum further into the quasi-nonlinear regime compared to one loop, up to $k_{\text{max}} \sim 0.1 \, h/{\text{Mpc}}$ at $z = 0$, but without reaching a high level of accuracy. In the case of the MPTbreeze method, we show that its bispectra decay at smaller and smaller scales with increasing loop order, but with smaller improvements. At three loops, this model predicts the bispectrum accurately up to scales $k_{\text{max}} \sim 0.17 \, h/{\text{Mpc}}$ at $z = 0$ and $k_{\text{max}} \sim 0.24 \, h/{\text{Mpc}}$ at $z = 1$.