Perturbation Theory Remixed II: Improved Modeling of Nonlinear Bispectrum

TL;DR

This paper introduces an improved nonlinear bispectrum modeling method called $n$-th order Eulerian Perturbation Theory ($n$EPT), which outperforms Standard Perturbation Theory (SPT) in accuracy and validity range for cosmological analyses.

Contribution

The paper demonstrates that $n$EPT provides more accurate bispectrum predictions than SPT across various scales and extends the validity range, especially for higher orders like 6EPT, in $w$CDM cosmologies.

Findings

$n$EPT bispectrum matches simulations better than SPT.

6EPT extends validity range to higher redshifts ($z extgreater1$).

Modeling accuracy depends on $\sigma_8(z)$ and grid resolution.

Abstract

We present the application of the $n$-th order Eulerian Perturbation Theory ($n$EPT) for modeling the matter bispectrum in real space as an advancement over the Standard Perturbation Theory (SPT). The $n$EPT method, detailed in Wang et al. (2023) \cite{Wang2023nEPT}, sums up the density perturbations up to the $n$-th order before computing summary statistics such as bispectrum. Taking advantage of grid-based calculation of SPT (GridSPT), we make a realization-based comparison of the analytical nonlinear bispectrum predictions from $n$EPT and SPT against a suite of $N$-body simulations. Using a spherical-bispectrum visualization scheme, we show that $n$EPT bispectrum matches better than SPT bispectrum over a wide range of scales in general $w$CDM cosmologies. Like the power spectrum case, we find that $n$EPT bispectrum modeling accuracy is controlled by $\sigma_8(z) \equiv \sigma_8 D(z)$, where $D(z)$ is the linear growth factor at a redshift $z$. Notably, the 6EPT doubles the bispectrum model's validity range compared to the one-loop SPT for $\sigma_8(z) < 0.5$, corresponding to redshifts $z\ge1$ for the best-fitting Planck-2018 cosmology. For $n\ge5$, however, $n$EPT bispectrum depends sensitively on the cut-off scale or the grid resolution. The percent-level modeling accuracy achieved for the spherical bispectrum (where we average over all triangular configurations) becomes much degraded when fixing configurations. Thus, we show that the validity range of the field-level cosmological inferences must be different from that derived from averaged summary statistics such as $n$-point correlation functions.