Comparing approximate methods for mock catalogues and covariance matrices III: Bispectrum

TL;DR

This study evaluates various approximate methods for generating dark matter halo catalogues by comparing their bispectrum measurements and covariance estimates against full N-body simulations, focusing on accuracy and impact on cosmological parameter errors.

Contribution

It systematically compares the accuracy of different approximate methods for bispectrum and covariance estimation against N-body simulations, highlighting their reliability and calibration needs.

Findings

Most methods achieve errors within 10% of N-body results.

Calibration is required for some methods, mainly for clustering amplitude.

Limited measurements can affect covariance estimates and parameter errors.

Abstract

We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and nonlinear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10% of the errors estimated from N-body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to two-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N-body simulation, and therefore to the bispectrum variance, by comparing with a larger set of several thousands realisations performed with one approximate method.