Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum

Abstract

When analyzing the galaxy bispectrum measured from spectroscopic surveys, it is imperative to account for the effects of non-uniform survey geometry. Conventionally, this is done by convolving the theory model with the the window function; however, the computational expense of this prohibits full exploration of the bispectrum likelihood. In this work, we provide a new class of estimators for the unwindowed bispectrum; a quantity that can be straightforwardly compared to theory. This builds upon the work of Philcox (2021) for the power spectrum, and comprises two parts (both obtained from an Edgeworth expansion): a cubic estimator applied to the data, and a Fisher matrix, which deconvolves the bispectrum components. In the limit of weak non-Gaussianity, the estimator is minimum-variance; furthermore, we give an alternate form based on FKP weights that is close-to-optimal and easy to compute. As a demonstration, we measure the binned bispectrum monopole of a suite of simulations both using conventional estimators and our unwindowed equivalents. Computation times are comparable, except that the unwindowed approach requires a Fisher matrix, computable in an additional $\mathcal{O}(100)$ CPU-hours. Our estimator may be straightforwardly extended to measure redshift-space distortions and the components of the bispectrum in arbitrary separable bases. The techniques of this work will allow the bispectrum to straightforwardly be included in the cosmological analysis of current and upcoming survey data.

arXiv comment31 pages, 8 figures, accepted by Phys. Rev. D. Code available at https://github.com/oliverphilcox/BOSS-Without-Windows

References in corpus (90)

• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• The 3D power spectrum of galaxies from the SDSS
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Power Spectrum Analysis of Three-Dimensional Redshift Surveys
• Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• The Cosmological Analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure
• Cosmological Parameters from the BOSS Galaxy Power Spectrum
• Estimating the Power Spectrum of the Cosmic Microwave Background
• How to measure CMB power spectra without losing information
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space
• Limits on non-Gaussianities from WMAP data
• Large-scale structure, the cosmic microwave background, and 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
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release
• Non-Linear Evolution of the Bispectrum of Cosmological Perturbations
• The Bispectrum as a Signature of Gravitational Instability in Redshift-Space
• Massive Lossless Data Compression and Multiple Parameter Estimation from Galaxy Spectra
• nbodykit: an open-source, massively parallel toolkit for large-scale structure
• Correcting for the alias effect when measuring the power spectrum using FFT
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Measuring the galaxy power spectrum with future redshift surveys
• The shape of primordial non-Gaussianity and the CMB bispectrum
• Non-linear perturbation theory extension of the Boltzmann code CLASS
• Fast Estimators for Redshift-Space Clustering
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Modeling the clustering and halo occupation distribution of BOSS-CMASS galaxies in the Final Data Release
• A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey
• Large-scale bias in the Universe: bispectrum method
• The Bispectrum: From Theory to Observations
• The power spectrum of galaxies in the 2dF 100k redshift survey
• The Bispectrum of IRAS Galaxies
• Blinded challenge for precision cosmology with large-scale structure: results from effective field theory for the redshift-space galaxy power spectrum
• The Bispectrum in the Effective Field Theory of Large Scale Structure
• A Fitting Formula for the Non-Linear Evolution of the Bispectrum
• An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps
• Constraining Primordial non-Gaussianity with Bispectrum and Power Spectum from Upcoming Optical and Radio Surveys
• Detection of Baryon Acoustic Oscillation Features in the Large-Scale 3-Point Correlation Function of SDSS BOSS DR12 CMASS Galaxies
• Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error
• Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in Fourier space
• Estimating non-gaussianity in the microwave background
• Algorithms for bispectra: forecasting, optimal analysis, and simulation
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures
• Optimal Estimation of Non-Gaussianity
• The large-scale 3-point correlation function of the SDSS BOSS DR12 CMASS galaxies
• Generalized massive optimal data compression
• Beyond the plane-parallel approximation for redshift surveys
• An optimal FFT-based anisotropic power spectrum estimator
• The Effect of Large-Scale Structure on the SDSS Galaxy Three-Point Correlation Function
• Eulerian BAO Reconstructions and N-Point Statistics
• A complete FFT-based decomposition formalism for the redshift-space bispectrum
• The Three-point Correlation Function of Galaxies Determined from the Las Campanas Redshift Survey
• Determining the Hubble Constant without the Sound Horizon: Measurements from Galaxy Surveys
• The Angular Power Spectrum of Galaxies from Early SDSS Data
• Galaxy Bias and Halo-Occupation Numbers from Large-Scale Clustering
• Near optimal bispectrum estimators for large-scale structure
• Primordial Non-Gaussianity from Biased Tracers: Likelihood Analysis of Real-Space Power Spectrum and Bispectrum
• A Detection of the Baryon Acoustic Oscillation Features in the SDSS BOSS DR12 Galaxy Bispectrum
• Three-point Correlation Functions of SDSS Galaxies in Redshift Space: Morphology, Color, and Luminosity Dependence
• 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
• Cosmology Without Windows: Quadratic Estimators for the Galaxy Power Spectrum
• The Large-Scale 3-point correlation function of SDSS Luminous Red Galaxies
• Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations
• 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
• Multiple Methods for Estimating the Bispectrum of the Cosmic Microwave Background with Application to the MAXIMA Data
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• Information content in the redshift-space galaxy power spectrum and bispectrum
• Modelling The Redshift-Space Three-Point Correlation Function in SDSS-III
• Capturing Non-Gaussianity of the Large-Scale Structure with Weighted Skew-Spectra
• Squared temperature-temperature power spectrum as a probe of the CMB bispectrum
• Fast Estimation of Gravitational and Primordial Bispectra in Large Scale Structures
• Constraining the Baryon-Dark Matter Relative Velocity with the Large-Scale 3-Point Correlation Function of the SDSS BOSS DR12 CMASS Galaxies
• Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation
• Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS Sample
• A Robust Measure of Cosmic Structure beyond the Power-Spectrum: Cosmic Filaments and the Temperature of Dark Matter
• Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints
• Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
• Universal Non-Gaussian Initial Conditions for N-body Simulations
• The Anisotropic Line Correlation Function as a Probe of Anisotropies in Galaxy Surveys
• Galaxy Skew-Spectra in Redshift-Space
• A Faster Fourier Transform? Computing Small-Scale Power Spectra and Bispectra for Cosmological Simulations in $\mathcal{O}(N^2)$ Time
• Towards cosmological constraints from the compressed modal bispectrum: a robust comparison of real-space bispectrum estimators
• Beyond Yamamoto: Anisotropic Power Spectra and Correlation Functions with Pairwise Lines-of-Sight
• An Inventory of Bispectrum Estimators for Redshift Space Distortions

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• Triumvirate: A Python/C++ package for three-point clustering measurements
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• Including relativistic and primordial Non-Gaussianity contributions in cosmological simulations by modifying the initial condition
• The size and shape dependence of the SDSS galaxy bispectrum
• Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements
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• Modeling and measuring the anisotropic halo 3-point correlation function: a coordinated study
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