Perturbation Theory vs Simulation: Quasi-linear Scale, Binning Effect,
  and Visualization of Bispectrum
  Recently, Perturbation Theory (PT), specifically the Effective Field Theory
of Large Scale Structure (EFTofLSS) and its equivalents, have proven powerful
in analyzing observational data. To further this pursuit, we present a
quantitative analysis for the accuracy of PT modeling by comparing its
analytical prediction to the result from a suite of Quijote simulations.
Specifically, we determine $k_{\rm NL}$, the wavenunmber below which the
analytical prediction matches well with the N-body result, for both leading
order (LO) and next-to-leading order (NLO) power spectrum and bispectrum at
redshifts $z=0$, $0.5$, $1$, $2$, $3$. We also quantify the binning effect in
Fourier space and show that an appropriate correction must be applied to the
analytic predictions in order to compare them with the discrete Fourier
transform results obtained from N-body-simulation or real data. Finally, we
have devised a novel spherical-Bispectrum visualization scheme fully capturing
the scale and configuration dependences. The new scheme facilitates
bispectrum-amplitude comparison, for example, between theory and N-body
results.
