Towards cosmological constraints from the compressed modal bispectrum: a robust comparison of real-space bispectrum estimators

TL;DR

This paper compares the standard and modal bispectrum estimators for galaxy clustering, demonstrating that the compressed modal approach provides consistent, efficient constraints with fewer parameters, and discusses robustness and sensitivity in the analysis pipeline.

Contribution

It introduces a robust comparison of real-space bispectrum estimators using simulations, highlighting the efficiency and reliability of the modal bispectrum method in cosmological parameter estimation.

Findings

Modal bispectrum yields constraints comparable to standard methods.

Only 6-10 modal coefficients suffice for equivalent constraints.

The pipeline's robustness to user settings and mock catalog variations is analyzed.

Abstract

Higher-order clustering statistics, like the galaxy bispectrum, can add complementary cosmological information to what is accessible with two-point statistics, like the power spectrum. While the standard way of measuring the bispectrum involves estimating a bispectrum value in a large number of Fourier triangle bins, the compressed modal bispectrum approximates the bispectrum as a linear combination of basis functions and estimates the expansion coefficients on the chosen basis. In this work, we compare the two estimators by using parallel pipelines to analyze the real-space halo bispectrum measured in a suite of $N$-body simulations corresponding to a total volume of $\sim 1{,}000 \,h^{-3}\,{\rm Gpc}^3$, with covariance matrices estimated from 10,000 mock halo catalogs. We find that the modal bispectrum yields constraints that are consistent and competitive with the standard bispectrum analysis: for the halo bias and shot noise parameters within the tree-level halo bispectrum model up to $k_{\rm max} \approx 0.06 \, (0.10) \,h\,{\rm Mpc}^{-1}$, only 6 (10) modal expansion coefficients are necessary to obtain constraints equivalent to the standard bispectrum estimator using $\sim$ 20 to 1,600 triangle bins, depending on the bin width. For this work, we have implemented a modal estimator pipeline using Markov Chain Monte Carlo simulations for the first time, and we discuss in detail how the parameter posteriors and modal expansion are robust to, or sensitive to, several user settings within the modal bispectrum pipeline. The combination of the highly efficient compression that is achieved and the large number of mock catalogs available allows us to quantify how our modal bispectrum constraints depend on the number of mocks that are used to estimate covariance matrices and the functional form of the likelihood.