The Integrated Bispectrum and Beyond

Abstract

The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the "soft limit" of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the {\em Hierarchical Ansatz} (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower order polyspectra with the same geometrical dependence but with {\em renormalised} amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field $\Theta$ and mixed multispectra involving $\delta$ and $\Theta$ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), for projected galaxy maps, convergence $\kappa$ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned $y$ - parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.

30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1407.1836 by other authors

References in corpus (46)

• SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems
• Halo Models of Large Scale Structure
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Transients from Initial Conditions in Cosmological Simulations
• The Effective Field Theory of Cosmological Large Scale Structures
• The WiggleZ Dark Energy Survey: Survey Design and First Data Release
• Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
• Cosmological parameters from lensing power spectrum and bispectrum tomography
• Transients from Initial Conditions: A Perturbative Analysis
• The Observed Squeezed Limit of Cosmological Three-Point Functions
• Super-Sample Covariance in Simulations
• Single-Field Consistency Relations of Large Scale Structure
• Galaxy Bias and non-Linear Structure Formation in General Relativity
• A Fitting Formula for the Non-Linear Evolution of the Bispectrum
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• An improved fitting formula for the dark matter bispectrum
• Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes
• A New Approach to Probing Primordial Non-Gaussianity
• Non-Linear Approximations to Gravitational Instability: A Comparison in the Quasi-Linear Regime
• The angle-averaged squeezed limit of nonlinear matter N-point functions
• From Weak Lensing to non-Gaussianity via Minkowski Functionals
• The full squeezed CMB bispectrum from inflation
• New Optimised Estimators for the Primordial Trispectrum
• Angular averaged consistency relations of large-scale structures
• Bias and Hierarchical Clustering
• Scaling in Gravitational Clustering, 2D and 3D Dynamics
• Kinematic consistency relations of large-scale structures
• Non-Gaussianity in Large Scale Structure and Minkowski Functionals
• From Snakes to Stars, the Statistics of Collapsed Objects - II. Testing a Generic Scaling Ansatz for Hierarchical Clustering
• From Snakes to Stars, the Statistics of Collapsed Objects - I. Lower--order Clustering Properties
• Weak Lensing from Strong Clustering
• CMB lensing and primordial squeezed non-Gaussianity
• Higher Order Statistics for Three-dimensional Shear and Flexion
• Testing the equal-time angular-averaged consistency relation of the gravitational dynamics in N-body simulations
• The Separate Universe Approach to Soft Limits
• Extracting the late-time kinetic Sunyaev-Zel'dovich effect
• 3D Weak Lensing: Modified Theories of Gravity
• Transients from Zel'dovich initial conditions
• Galaxy Clustering in 3D and Modified Gravity Theories
• Lensing-induced morphology changes in CMB temperature maps in modified gravity theories
• Statistical Properties of Thermal Sunyaev-Zel'dovich Maps
• Cross-correlating Sunyaev-Zel'dovich and Weak Lensing Maps
• Redshift-space equal-time angular-averaged consistency relations of the gravitational dynamics
• Reionization and CMB non-Gaussianity
• Direct mechanism in solar nuclear reactions

Cited by in corpus (21)

• The integrated 3-point correlation function of cosmic shear
• Self-calibration of weak lensing systematic effects using combined two- and three-point statistics
• Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
• What Can We Learn by Combining the Skew Spectrum and the Power Spectrum?
• Weak lensing mass reconstruction using sparsity and a Gaussian random field
• Sparse Bayesian mass-mapping with uncertainties: local credible intervals
• Cosmology from the integrated shear 3-point correlation function: simulated likelihood analyses with machine-learning emulators
• Higher multipoles of the galaxy bispectrum in redshift space
• Sparse Bayesian mass-mapping with uncertainties: peak statistics and feature locations
• Consistency Relations in Effective Field Theory
• Estimating the Integrated Bispectrum from Weak Lensing Maps
• The integrated angular bispectrum of weak lensing
• The integrated angular bispectrum
• Constraints on primordial non-Gaussianity using multitracer technique for skew spectrum
• Position-Dependent Correlation Function of Weak Lensing Convergence
• Generative modelling for mass-mapping with fast uncertainty quantification
• Three-flavor, Full Momentum Space Neutrino Spin Oscillations in Neutron Star Mergers
• Neutrino flavor instabilities in neutron star mergers with moment transport: Slow, fast, and collisional modes
• Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
• On Weak Lensing Response Functions
• Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure