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 at the quasi-linear 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 further put forward the approach by taking the redshift-space distortions into account. With the new implementation, we have, for the first time, generated the redshift-space density field to the fifth order and computed the next-to-next-to-leading order (2 loop) power spectrum and the next-to-leading order (1 loop) bispectrum of matter clustering in redshift space. By comparing the result with corresponding analytical SPT calculation and N -body simulations, we find that the SPT calculation (A) suffers much more from the UV sensitivity due to the higher-derivative operators and (B) deviates from the N -body results from the Fourier wavenumber smaller than real space kmax. Finally, we have shown that while Padé approximation removes spurious features in morphology, it does not improve the modeling of power spectrum and bispectrum.

Reconstructing the long-wavelength matter density fluctuation modes from the scalar-type clustering fossils

“…To assess the requirement for a robust reconstruction method, we take a simpler approach here. Namely, instead of analyzing the result from full N -body simulations, we test the reconstruction method against a controlled sample density field only containing the first-and second-order density perturbations from the GridSPT (grid-based calculation of standard perturbation theory) [53][54][55]. Because the GridSPT density field strictly follows SPT, the fossil estimator constructed from the leading-order bispectrum can fully capture the coupling between the long and short modes.…”