An Inventory of Bispectrum Estimators for Redshift Space Distortions

Abstract

In order to best improve constraints on cosmological parameters and on models of modified gravity using current and future galaxy surveys it is necessary maximally exploit the available data. As redshift-space distortions mean statistical translation invariance is broken for galaxy observations, this will require measurement of the monopole, quadrupole and hexadecapole of not just the galaxy power spectrum, but also the galaxy bispectrum. A recent (2015) paper by Scoccimarro demonstrated how the standard bispectrum estimator may be expressed in terms of Fast Fourier Transforms (FFTs) to afford an extremely efficient algorithm, allowing the bispectrum multipoles on all scales and triangle shapes to be measured in comparable time to those of the power spectrum. In this paper we present a suite of alternative proxies to measure the three-point correlation multipoles. In particular, we describe a modal (or plane wave) decomposition to capture the information in each multipole in a series of basis coefficients, and also describe three compressed estimators formed using the skew-spectrum, the line correlation function and the integrated bispectrum, respectively. As well as each of the estimators offering a different measurement channel, and thereby a robustness check, it is expected that some (especially the modal estimator) will offer a vast data compression, and so a much reduced covariance matrix. This compression may be vital to reduce the computational load involved in extracting the available three-point information.

14 pages

References in corpus (12)

• The DESI Experiment Part I: Science,Targeting, and Survey Design
• The Effective Field Theory of Cosmological Large Scale Structures
• Cosmology and the Bispectrum
• The IR-resummed Effective Field Theory of Large Scale Structures
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• Near optimal bispectrum estimators for large-scale structure
• Redshift Space Distortions in the Effective Field Theory of Large Scale Structures
• Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum
• Towards optimal cosmological parameter recovery from compressed bispectrum statistics
• A Robust Measure of Cosmic Structure beyond the Power-Spectrum: Cosmic Filaments and the Temperature of Dark Matter
• Cosmology with Phase Statistics: Parameter Forecasts and Detectability of BAO
• The bias of galaxies and the density of the universe from the 2dF galaxy redshift survey

Cited by in corpus (6)

• Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum
• Modal compression of the redshift-space galaxy bispectrum
• Towards cosmological constraints from the compressed modal bispectrum: a robust comparison of real-space bispectrum estimators
• Testing the equivalence principle on cosmological scales using the odd multipoles of galaxy cross-power spectrum and bispectrum
• The Impact of ionization Morphology and X-ray Heating on the Cosmological 21cm Skew Spectrum
• Studying Interstellar Turbulence Driving Scales using the Bispectrum