Toward Accurate Modeling of the Nonlinear Matter Bispectrum: Standard Perturbation Theory and Transients from Initial Conditions

TL;DR

This paper evaluates the accuracy of nonlinear matter bispectrum modeling using simulations and perturbation theory, emphasizing initial conditions and the validity of various analytical formulas across redshifts.

Contribution

It demonstrates the importance of initial condition choices in simulations and compares analytical models, identifying regimes where each provides accurate predictions.

Findings

2LPT initial conditions with high redshift reduce transients.

One-loop standard perturbation theory matches N-body results at high redshift.

Different empirical fitting formulas perform best at different redshifts.

Abstract

Accurate modeling of nonlinearities in the galaxy bispectrum, the Fourier transform of the galaxy three-point correlation function, is essential to fully exploit it as a cosmological probe. In this paper, we present numerical and theoretical challenges in modeling the nonlinear bispectrum. First, we test the robustness of the matter bispectrum measured from N-body simulations using different initial conditions generators. We run a suite of N-body simulations using the Zel'dovich approximation and second-order Lagrangian perturbation theory (2LPT) at different starting redshifts, and find that transients from initial decaying modes systematically reduce the nonlinearities in the matter bispectrum. To achieve 1% accuracy in the matter bispectrum for $z\le3$ on scales $k<1$ $h$/Mpc, 2LPT initial conditions generator with initial redshift of $z\gtrsim100$ is required. We then compare various analytical formulas and empirical fitting functions for modeling the nonlinear matter bispectrum, and discuss the regimes for which each is valid. We find that the next-to-leading order (one-loop) correction from standard perturbation theory matches with N-body results on quasi-linear scales for $z\ge1$. We find that the fitting formula in Gil-Mar\'{\i}n et al. (2012) accurately predicts the matter bispectrum for $z\le1$ on a wide range of scales, but at higher redshifts, the fitting formula given in Scoccimarro & Couchman (2001) gives the best agreement with measurements from N-body simulations.