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