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

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 kmax. 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.