Comparing approximate methods for mock catalogues and covariance matrices II: Power spectrum multipoles

TL;DR

This study evaluates the accuracy of seven approximate methods for modeling halo power spectrum multipoles and their covariances, assessing their impact on cosmological parameter constraints compared to full N-body simulations.

Contribution

It provides a comprehensive benchmark of various approximate methods for power spectrum multipoles and covariance estimation, highlighting their accuracy and limitations.

Findings

Most methods reproduce the monopole within 5%.

Residuals for the quadrupole can be larger and scale-dependent.

Covariance estimates from approximate methods yield parameter errors within 10% of N-body results.

Abstract

We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constrains related to growth rate of structure, Alcock-Paczynski distortions and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE-COLA, Pinocchio and PeakPatch), methods that rely on halo assignment schemes onto dark-matter overdensities calibrated with a target N-body run (Halogen, Patchy) and two standard assumptions about the full density PDF (Gaussian and Lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5\%$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10\%$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10\%$ of those from the N-body based covariance.