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

TL;DR

This paper introduces a grid-based perturbation theory method to compute redshift-space matter fluctuations up to fifth order, revealing UV sensitivities and limitations of Padé approximations in modeling large-scale structure.

Contribution

The authors developed the GridSPT algorithm for redshift-space calculations and demonstrated its ability to generate higher-order density fields and spectra, highlighting UV sensitivities and modeling challenges.

Findings

SPT calculation shows high UV sensitivity due to higher-derivative operators.

Deviations from N-body simulations occur at scales smaller than real space k_max.

Padé approximation does not improve power spectrum and bispectrum modeling.

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 $k_{\rm max}$. Finally, we have shown that while Pad\'e approximation removes spurious features in morphology, it does not improve the modeling of power spectrum and bispectrum.