The Angular Trispectra of CMB Temperature and Polarization

Abstract

We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization fields. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB fields, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by inflationary models. Due to the large number of four-point configurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced for example by the gravitational lensing of the CMB by the large scale structure of the universe.

16 pages, 4 figures; typographical errors corrected

References in corpus (5)

• The Angular Trispectrum of the CMB
• Non-Gaussianity from Inflation
• Dark Synergy: Gravitational Lensing and the CMB
• Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps
• The Trispectrum of the 4 Year COBE-DMR data

Cited by in corpus (133)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Non-Gaussianity from Inflation: Theory and Observations
• Weak Gravitational Lensing of the CMB
• The inflationary prediction for primordial non-gaussianity
• Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• Non-Gaussianity of the primordial perturbation in the curvaton model
• Large Non-Gaussianities in Single Field Inflation
• Measuring primordial non-Gaussianity in the cosmic microwave background
• Galileon inflation
• Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background
• Correlation of CMB with large-scale structure: II. Weak lensing
• Primordial trispectrum from inflation
• Detecting a small perturbation through its non-Gaussianity
• Review of local non-Gaussianity from multi-field inflation
• Angular Trispectrum of CMB Temperature Anisotropy from Primordial Non-Gaussianity with the Full Radiation Transfer Function
• The Inflationary Trispectrum for Models with Large Non-Gaussianities
• The inflationary trispectrum
• 3D weak lensing
• Primordial non-Gaussianity, scale-dependent bias, and the bispectrum of galaxies
• Multiple field inflation
• Primordial Non-Gaussianity and Analytical Formula for Minkowski Functionals of the Cosmic Microwave Background and Large-scale Structure
• CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation
• CMB Anisotropies at Second Order I
• Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background
• CMB Anisotropies at Second-Order II: Analytical Approach
• Reconstructing Patchy Reionization from the Cosmic Microwave Background
• Non-Gaussianity beyond slow roll in multi-field inflation
• General CMB and Primordial Trispectrum Estimation
• Signature of primordial non-Gaussianity of phi^3-type in the mass function and bias of dark matter haloes
• Non-gaussianity from the inflationary trispectrum
• Non-Gaussianity and statistical anisotropy from vector field populated inflationary models
• Estimators for local non-Gaussianities
• The curvature perturbation in a box
• Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
• Non-gaussianity and cosmic uncertainty in curvaton-type models
• Cross-correlation of CMB with large-scale structure: weak gravitational lensing
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Primordial Non-Gaussianity in the Cosmic Microwave Background
• A Naturally Large Four-Point Function in Single Field Inflation
• Non Gaussianity and Minkowski Functionals: forecasts for Planck
• Non-Gaussianity in Two-Field Inflation
• The Full Second-Order Radiation Transfer Function for Large-Scale CMB Anisotropies
• Non-Gaussianity and the Cosmic Microwave Background Anisotropies
• Diagrammatic approach to non-Gaussianity from inflation
• The Trispectrum in the Effective Field Theory of Large Scale Structure
• The Non-Gaussian Halo Mass Function with fNL, gNL and tauNL
• Reconstruction of the remote dipole and quadrupole fields from the kinetic Sunyaev Zel'dovich and polarized Sunyaev Zel'dovich effects
• The Odd-Parity CMB Bispectrum
• On the full quantum trispectrum in multi-field DBI inflation
• Lorentz boost and non-Gaussianity in multi-field DBI-inflation
• The trispectrum of 21-cm background anisotropies as a probe of primordial non-Gaussianity
• Primordial Magnetic Field Limits from CMB Trispectrum - Scalar Modes and Planck Constraints
• Galaxy-CMB and galaxy-galaxy lensing on large scales: sensitivity to primordial non-Gaussianity
• Combined local and equilateral non-Gaussianities from multifield DBI inflation
• Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model
• Non-gaussianity in axion Nflation models
• Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits
• Inflationary trispectrum from graviton exchange
• Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations
• Landscape tomography through primordial non-Gaussianity
• Large Primordial Trispectra in General Single Field Inflation
• Anisotropic Trispectrum of Curvature Perturbations Induced by Primordial Non-Abelian Vector Fields
• Halo clustering and g_{NL}-type primordial non-Gaussianity
• The Signature of Patchy Reionization in the Polarization Anisotropy of the CMB
• A non-Gaussian landscape
• Super-Sample CMB Lensing
• Non-Gaussianity of scalar perturbations generated by conformal mechanisms
• Signatures of anisotropic sources in the trispectrum of the cosmic microwave background
• Lensing reconstruction from PLANCK sky maps: inhomogeneous noise
• Consistency conditions and primordial black holes in single field inflation
• Limits on Second-Order Non-Gaussianity from Minkowski Functionals of WMAP Data
• On Non-Gaussianities in Multi-Field Inflation (N fields): Bi- and Tri-spectra beyond Slow-Roll
• Non-Gaussian corrections to the probability distribution of the curvature perturbation from inflation
• CMB lensing extraction and primordial non-Gaussianity
• Feeding your Inflaton: Non-Gaussian Signatures of Interaction Structure
• Seeking Inflation Fossils in the Cosmic Microwave Background
• Kinetic Sunyaev Zeldovich effect in an anisotropic CMB model: measuring low multipoles of the CMB at higher redshifts using intensity and polarization spectral distortions
• The CMB Bispectrum, Trispectrum, non-Gaussianity, and the Cramer-Rao Bound
• The Detectability of Departures from the Inflationary Consistency Equation
• CMB Lensing Constraints on Dark Energy and Modified Gravity Scenarios
• Isotropic N-Point Basis Functions and Their Properties
• CMB Constraints on the Stochastic Gravitational-Wave Background at Mpc scales
• Efficient diagrammatic computation method for higher order correlation functions of local type primordial curvature perturbations
• Lensed CMB temperature and polarization maps from the Millennium Simulation
• Non-Gaussianity of Large-Scale Cosmic Microwave Background Anisotropies beyond Perturbation Theory
• CMB lensing and primordial squeezed non-Gaussianity
• Analysis of non-Gaussian CMB maps based on the N-pdf. Application to WMAP data
• Higher Order Statistics for Three-dimensional Shear and Flexion
• Evidence for the Cross-correlation between Cosmic Microwave Background Polarization Lensing from POLARBEAR and Cosmic Shear from Subaru Hyper Suprime-Cam
• Non-gaussianity in axion N-flation models: detailed predictions and mass spectra
• General and consistent statistics for cosmological observations
• Non-Gaussian Mode Coupling and the Statistical Cosmological Principle
• Optimizing future experimental probes of inflation
• Trispectrum estimation in various models of equilateral type non-Gaussianity
• Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum
• Planck Trispectrum Constraints on Primordial Non-Gaussianity at Cubic Order
• Cosmic polarimetry in magnetoactive plasmas
• Real-world CMB lensing quadratic estimator power spectrum response
• 3D cosmic shear: numerical challenges, 3D lensing random fields generation and Minkowski Functionals for cosmological inference
• The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum
• Parameter constraints from weak lensing tomography of galaxy shapes and cosmic microwave background fluctuations
• Constraining the WMAP9 bispectrum and trispectrum with needlets
• The effects on CMB power spectra and bispectra from the polarization rotation and its correlations with temperature and E-polarization
• Probing parity-odd bispectra with anisotropies of GW $V$ modes
• Multipoint correlators in multifield cosmology
• Angular bispectrum and trispectrum of scalar-induced gravitational waves: all contributions from primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$
• Probing the primordial Universe with 21-cm line from cosmic dawn/epoch of reionization
• Cosmology with the Square Kilometre Array by SKA-Japan
• An Observational Test of Holographic Inflation
• CMB temperature anisotropies from third order gravitational perturbations
• Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
• Constraints on ${\tau }_{\mathrm{NL}}$ from Planck temperature and polarization
• Scale Dependence of the Halo Bias in General Local-Type Non-Gaussian Models I: Analytical Predictions and Consistency Relations
• Impact of nonlinear growth of the large-scale structure on CMB B-mode delensing
• Isotropic non-Gaussian $g_{\mathrm{NL}}$-like toy models that reproduce the cosmic microwave background anomalies
• Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic
• Statistical anisotropies in temperature and polarization fluctuations from a scale-dependent trispectrum
• Applications of High Resolution High Sensitivity Observations of the CMB
• The interplay of CMB temperature lensing power reconstruction with primordial non-Gaussianity of local type
• Higher-Order Spectra of Weak Lensing Convergence Maps in Parameterized Theories of Modified Gravity
• Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models
• CMB B-mode polarization from Thomson scattering in the local universe
• The Halo Mass Function from Excursion Set Theory with a Non-Gaussian Trispectrum
• Primordial Black Holes in non-linear perturbation theory
• The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation
• Cosmological correlation functions in scalar and vector inflationary models
• Measuring CMB non-Gaussianity as a probe of Inflation and Cosmic Strings
• Filtering of Continuous Time Periodically Correlated Isotropic Random Fields
• The shape of high order correlation functions in CMB anisotropy maps
• Trispectrum and higher order spectra for non-Gaussian homogenous and isotropic field on the 2D-plane
• Non-Gaussian likelihood of weak lensing power spectra