Modal compression of the redshift-space galaxy bispectrum

TL;DR

This paper extends the modal decomposition method to the anisotropic redshift-space galaxy bispectrum, demonstrating it efficiently captures the full information content with fewer coefficients compared to other basis decompositions.

Contribution

It introduces an extension of the modal decomposition approach to redshift-space bispectrum and compares its efficiency with spherical and tripolar harmonic decompositions.

Findings

Modal decomposition captures over 90% of full bispectrum information with only 14 coefficients.

Modal method outperforms spherical harmonic multipoles in efficiency.

All three methods recover the full information content effectively.

Abstract

We extend the modal decomposition method, previously applied to compress the information in the real-space bispectrum, to the anisotropic redshift-space galaxy bispectrum. In the modal method approach, the bispectrum is expanded on a basis of smooth functions of triangles and their orientations, such that a set of modal expansion coefficients can capture the information in the bispectrum. We assume a reference survey and compute Fisher forecasts for the compressed modal bispectrum and two other basis decompositions of the redshift-space bispectrum in the literature, one based on (single) spherical harmonics and another based on tripolar spherical harmonics. In each case, we compare the forecasted constraints from the compressed statistic with forecasted constraints from the full, uncompressed bispectrum which includes all triangles and orientations. Our main result is that all three compression methods achieve good recovery of the full information content of the bispectrum, but the modal decomposition approach achieves this the most efficiently: only 14 (42) modal expansion coefficients are necessary to obtain constraints that are within 10% (2%) of the full bispectrum result. The next most efficient decomposition is the one based on tripolar spherical harmonics, while the spherical harmonic multipoles are the least efficient.