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

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 $\sim 1,000h^{-3}{\mathrm{Gpc}}^3$, 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 $k_{\max }\approx 0.06(0.10)h{\mathrm{Mpc}}^{-1}$, 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.

arXiv comment51 pages, 20 figures, 2 tables. To be submitted to JCAP. Comments are welcome

References in corpus (76)

• emcee: The MCMC Hammer
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Cuba - a library for multidimensional numerical integration
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies
• Massive Lossless Data Compression and Multiple Parameter Estimation from Galaxy Spectra
• Parameter inference with estimated covariance matrices
• PINOCCHIO: pinpointing orbit-crossing collapsed hierarchical objects in a linear density field
• Accurate Estimators of Correlation Functions in Fourier Space
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Cosmology with the SPHEREX All-Sky Spectral Survey
• Systematic Bias in Cosmic Shear: Beyond the Fisher Matrix
• The Impact of Inhomogeneous Reionization on Cosmic Microwave Background Anisotropy
• General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL
• Gaussian covariance matrices for anisotropic galaxy clustering measurements
• Constraining Primordial non-Gaussianity with Bispectrum and Power Spectum from Upcoming Optical and Radio Surveys
• Constraining $M_{\nu }$ with the Bispectrum I: Breaking Parameter Degeneracies
• An accurate tool for the fast generation of dark matter halo catalogs
• Detection of Baryon Acoustic Oscillation Features in the Large-Scale 3-Point Correlation Function of SDSS BOSS DR12 CMASS Galaxies
• Cosmological information in the redshift-space bispectrum
• Galaxy Power Spectrum Multipoles Covariance in Perturbation Theory
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• Optimal Estimation of Non-Gaussianity
• Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time
• The large-scale 3-point correlation function of the SDSS BOSS DR12 CMASS galaxies
• Assessment of the Information Content of the Power Spectrum and Bispectrum
• The CMB Bispectrum
• A complete FFT-based decomposition formalism for the redshift-space bispectrum
• Galaxy bispectrum, primordial non-Gaussianity and redshift space distortions
• Near optimal bispectrum estimators for large-scale structure
• Comparing approximate methods for mock catalogues and covariance matrices III: Bispectrum
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies II: cosmological interpretation
• A Detection of the Baryon Acoustic Oscillation Features in the SDSS BOSS DR12 Galaxy Bispectrum
• Improving fast generation of halo catalogs with higher-order Lagrangian perturbation theory
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• Fewer Mocks and Less Noise: Reducing the Dimensionality of Cosmological Observables with Subspace Projections
• Galaxy redshift-space bispectrum: the Importance of Being Anisotropic
• Perturbative approach to covariance matrix of the matter power spectrum
• DEMNUni: Massive neutrinos and the bispectrum of large scale structures
• Toward a robust inference method for the galaxy bispectrum: likelihood function and model selection
• Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum
• Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
• A fast estimator for the bispectrum and beyond - A practical method for measuring non-Gaussianity in 21-cm maps
• A Practical Computational Method for the Anisotropic Redshift-Space 3-Point Correlation Function
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations
• Information content in the redshift-space galaxy power spectrum and bispectrum
• Capturing Non-Gaussianity of the Large-Scale Structure with Weighted Skew-Spectra
• Towards optimal cosmological parameter recovery from compressed bispectrum statistics
• Fast Estimation of Gravitational and Primordial Bispectra in Large Scale Structures
• The one-loop matter bispectrum as a probe of gravity and dark energy
• Cosmology with anisotropic galaxy clustering from the combination of power spectrum and bispectrum
• Non-linear shrinkage estimation of large-scale structure covariance
• Non-Gaussianity in Large Scale Structure and Minkowski Functionals
• A Robust Measure of Cosmic Structure beyond the Power-Spectrum: Cosmic Filaments and the Temperature of Dark Matter
• Constraining modified theory of gravity with galaxy bispectrum
• Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints
• Galaxy 2-Point Covariance Matrix Estimation for Next Generation Surveys
• Estimating the power spectrum covariance matrix with fewer mock samples
• Non-Linear Matter Power Spectrum Covariance Matrix Errors and Cosmological Parameter Uncertainties
• Universal Non-Gaussian Initial Conditions for N-body Simulations
• Three-point phase correlations: A new measure of non-linear large-scale structure
• Covariance of the matter power spectrum including the survey window function effect: N-body simulations vs. fifth-order perturbation theory on grid
• A Bayesian method for combining theoretical and simulated covariance matrices for large-scale structure surveys
• The Anisotropic Line Correlation Function as a Probe of Anisotropies in Galaxy Surveys
• Cosmology with Phase Statistics: Parameter Forecasts and Detectability of BAO
• Modelling the matter bispectrum at small scales in modified gravity
• Extreme data compression while searching for new physics
• Matter bispectrum of large-scale structure with Gaussian and non-Gaussian initial conditions: Halo models, perturbation theory, and a three-shape model
• GEOMAX: beyond linear compression for 3pt galaxy clustering statistics
• An Inventory of Bispectrum Estimators for Redshift Space Distortions
• Probing redshift-space distortions with phase correlations
• Cosmological Constraints from Fourier Phase Statistics
• Constraining the growth rate of structure with phase correlations

Cited by in corpus (10)

• Constraints on Multi-Field Inflation from the BOSS Galaxy Survey
• Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum
• The Covariance of Squeezed Bispectrum Configurations
• Quijote-PNG: Quasi-maximum likelihood estimation of Primordial Non-Gaussianity in the non-linear dark matter density field
• Modal compression of the redshift-space galaxy bispectrum
• Quantification of high dimensional non-Gaussianities and its implication to Fisher analysis in cosmology
• A fast estimator for quantifying the shape dependence of the 3D bispectrum
• Quijote-PNG: Quasi-maximum likelihood estimation of Primordial Non-Gaussianity in the non-linear halo density field
• The halo 3-point correlation function: a methodological analysis
• Mixing Bispectrum Multipoles Under Geometric Distortions