Grid-based calculations of redshift-space matter fluctuations from perturbation theory: UV sensitivity and convergence at the field level

Abstract

Perturbation theory (PT) has been used to interpret the observed nonlinear large-scale structure statistics in the quasilinear regime. To facilitate the PT-based analysis, we have presented the GridSPT algorithm, a grid-based method to compute the nonlinear density and velocity fields in standard perturbation theory (SPT) from a given linear power spectrum. Here, we expand on this approach by taking the redshift-space distortions into account. With the new implementation, we generate for the first time the redshift-space density field to the fifth order and computed the next-to-next-to-leading-order (two-loop) power spectrum and the next-to-leading-order (one-loop) bispectrum of matter clustering in redshift space. By comparing the result with the corresponding analytical SPT calculation and N-body simulations, we find that the SPT calculation (A) suffers much more from UV sensitivity due to the higher-derivative operators, and (B) deviates from the N-body results above the Fourier wave number smaller than real space k[max]. Finally, we show that while the Padé approximation removes spurious features in the morphology, it does not improve the modeling of the power spectrum and bispectrum.