Perturbation Theory Remixed II: Improved Modeling of Nonlinear Bispectrum

We present the application of the n-th order Eulerian Perturbation Theory (nEPT) for modeling the matter bispectrum in real space as an advancement over the Standard Perturbation Theory (SPT). The nEPT method, detailed in Wang et al. (2023) {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 nEPT and SPT against a suite of N-body simulations. Using a spherical-bispectrum visualization scheme, we show that nEPT bispectrum matches better than SPT bispectrum over a wide range of scales in general wCDM cosmologies. Like the power spectrum case, we find that nEPT bispectrum modeling accuracy is controlled by σ₈(z) ≡ σ₈ 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 σ₈(z) < 0.5, corresponding to redshifts z≥1 for the best-fitting Planck-2018 cosmology. For n≥5, however, nEPT 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.