Statistics of Cosmic Microwave Background Polarization

Abstract

We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.

28 pages, RevTeX

References in corpus (4)

• An All-Sky Analysis of Polarization in the Microwave Background
• Signature of Gravity Waves in Polarization of the Microwave Background
• A Probe of Primordial Gravity Waves and Vorticity
• Polarization of the Microwave Background in Reionized Models

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• Foreground model recognition through Neural Networks for CMB B-mode observations
• Probing the largest scale structure in the universe with polarization map of galaxy clusters
• Relic gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission
• CMB in a box: causal structure and the Fourier-Bessel expansion
• Lack-of-correlation anomaly in CMB large scale polarisation maps
• CMB $V$ modes from photon-photon forward scattering revisited
• New probe of magnetic fields in the prereionization epoch. I. Formalism
• 3D weak lensing with spin wavelets on the ball
• A wavelet-Galerkin algorithm of the E/B decomposition of CMB polarization maps
• Design and characterization of the Cosmology Large Angular Scale Surveyor (CLASS) 93 GHz focal plane
• Is Cosmology Compatible with Blue Gravity Waves ?
• E and B polarizations from inhomogeneous and solar surface turbulence
• Circular polarization in a spherical basis
• Inflamagnetogenesis redux: Unzipping sub-Planckian inflation via various cosmoparticle probes
• Measuring the Homogeneity of the Universe Using Polarization Drift
• Detecting Relic Gravitational Waves in the CMB: Comparison of Planck and Ground-based Experiments
• Polarization Signal of Distant Clusters and Reconstruction of Primordial Potential Fluctuations
• Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge
• Primordial quadrupole-induced polarisation from filamentary structures and galaxy clusters
• Impact of half-wave plate systematics on the measurement of cosmic birefringence from CMB polarization
• Constraining gravity with a new precision $E_G$ estimator using Planck + SDSS BOSS
• First attempt at measuring the CMB cross-polarization
• Lyman-$\alpha$ Polarization Intensity Mapping
• PAPPA: Primordial Anisotropy Polarization Pathfinder Array
• E/B Separation in CMB Interferometry
• Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings
• Full-sky beam convolution for cosmic microwave background applications
• Mapping dark matter on the celestial sphere with weak gravitational lensing
• Thomson scattering: One rate to rule them all
• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems
• Implementation of a Fourier Matched Filter in CMB Analyses. Application to ISW Studies
• Relic Gravitational Waves And CMB Polarization In The Accelerating Universe
• Introduction to neutrino cosmology
• Estimating the tensor-to-scalar ratio and the effect of residual foreground contamination
• Using pulsar timing arrays and the quantum normalization condition to constrain relic gravitational waves
• The effects on CMB power spectra and bispectra from the polarization rotation and its correlations with temperature and E-polarization
• Limits on the Polarization of the Cosmic Microwave Background Radiation at Multipoles up to l~2000
• Real space lensing reconstruction using cosmic microwave background polarization
• Separating E from B
• Correlations Between the WMAP and MAXIMA Cosmic Microwave Background Anisotropy Maps
• Chasing cosmic inflation: constraints for inflationary models and reheating insights
• A Strategy to Minimize Dust Foregrounds in B-mode Searches
• Parameter extraction by Planck for a CDM model with broken scale invariance and cosmological constant
• Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix
• Primordial Gravitational Waves Assisted by Cosmological Scalar Perturbations
• Testing CMB Anomalies in E-mode Polarization with Current and Future Data
• Analysis method for 3D power spectrum of projected tensor field with fast estimator and window convolution modelling: an application to intrinsic alignments
• A galaxy-free phenomenological model for the 21-cm power spectrum during reionization
• A theoretical estimate of intrinsic ellipticity bispectra induced by angular momenta alignments
• CMB Polarization and Temperature Power Spectra Estimation using Linear Combination of WMAP 5-year Maps
• Effects of Destriping Errors on CMB Polarisation Power Spectra and and Pixel Noise Covariances
• Reconstructing Cosmic Polarization Rotation with ResUNet-CMB
• Mimetic DBI Inflation in Confrontation with Planck2018 data
• Generation of Circular Polarization of CMB via Polarized Compton Scattering
• On the asymptotic connection between full- and flat-sky angular correlators
• Mitigating Foreground Bias to the CMB Lensing Power Spectrum for a CMB-HD Survey
• An Examination of Galactic Polarization with Application to the Planck TB Correlation
• Real-space computation of $E$/$B$-mode maps I: Formalism, Compact Kernels, and Polarized Filaments
• Measuring the Energy Scale of Inflation with Large Scale Structures
• Phase-transition sound of inflation at gravitational waves detectors
• CMB B-mode auto-bispectrum produced by primordial gravitational waves
• Is patchy reionization an obstacle in detecting the primordial gravitational wave signal?
• Morphological Analysis of the Polarized Synchrotron Emission with WMAP and Planck
• Wigner-Eckart theorem in cosmology: Bispectra for total-angular-momentum waves
• Lensing-induced morphology changes in CMB temperature maps in modified gravity theories
• Foreground Bias From Parametric Models of Far-IR Dust Emission
• LiteBIRD Science Goals and Forecasts: A full-sky measurement of gravitational lensing of the CMB
• An angular power spectrum analysis of the DRAO 1.4 GHz polarization survey: implications for CMB observations
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
• E and B families of the Stokes parameters in the polarized synchrotron and thermal dust foregrounds
• Detection and Removal of B-mode Dust Foregrounds with Signatures of Statistical Anisotropy
• Impact of Instrumental Systematic Contamination on the Lensing Mass Reconstruction using the CMB Polarization
• Concept Design of Low Frequency Telescope for CMB B-mode Polarization satellite LiteBIRD
• Probing primordial features with the primary CMB
• Gravitational waves in neutrino plasma and NANOGrav signal
• CMB polarization as a tool to constrain the optical properties of the Universe
• Detecting primordial gravitational waves with circular polarization of the redshifted 21 cm line: I. Formalism
• CMB Polarization at Large Angular Scales: Data Analysis of the POLAR Experiment
• Dark Energy and Inflation in a Gravitational Wave Dominated Universe
• Revisit relic gravitational waves based on the latest CMB observations
• Relic gravitational waves in the frame of slow-roll inflation with a power-law potential and the detection
• Robust constraints on tensor perturbations from cosmological data: a comparative analysis from Bayesian and frequentist perspectives
• Differentiable and accelerated spherical harmonic and Wigner transforms
• The History of Inflation from Microwave Background Polarimetry and Laser Interferometry
• Polarization Diffusion from Spacetime Uncertainty
• The shape of CMB temperature and polarization peaks on the sphere
• Self-accelerating Massive Gravity: Hidden Constraints and Characteristics
• Nonlinear electrodynamics and CMB polarization
• Mosaicking with cosmic microwave background interferometers
• Approximate Consistency Condition from Running Spectral Index in Slow-Roll Inflationary Models
• Real space tomography of the primordial Universe with cluster polarization
• Polarized Spots in Anisotropic Open Universes
• Needlet thresholding methods in component separation
• Missing baryons, bulk flows and the E-mode polarization of the Cosmic Microwave Background
• CMB anisotropies induced by tensor modes in Massive Gravity
• Direct reconstruction of spherical harmonics from interferometer observations of the CMB polarization
• Detecting primordial gravitational waves with circular polarization of the redshifted 21 cm line: II. Forecasts
• STARS: A software application for the EBEX autonomous daytime star cameras
• Cross-correlation between $Planck$ CMB lensing potential and galaxy catalogues from HELP
• Spin Needlets for Cosmic Microwave Background Polarization Data Analysis
• Gravitational lensing of the cosmic microwave background by nonlinear structures
• Why CMB physics?
• Delensing of Cosmic Microwave Background Polarization with machine learning
• Cosmological Inflation and Meta-Empirical Theory Assessment
• Fingerprint of Galactic Loop I on polarized microwave foregrounds
• Temperature and Polarization Patterns in Anisotropic Cosmologies
• Multiple Field Inflation and Signatures of Heavy Physics in the CMB
• CMB Telescopes and Optical Systems
• Forecast of cross-correlation of CSST cosmic shear tomography with AliCPT-1 CMB lensing
• The consistency relation in braneworld inflation
• The PICASSO map-making code: application to a simulation of the QUIJOTE northern sky survey
• New Interpretations of the Cosmological Preference for a Negative Neutrino Mass
• How well do third-order aperture mass statistics separate E- and B-modes?
• Optimal and fast E/B separation with a dual messenger field
• Gravitational waves, CMB polarization, and the Hubble tension
• Mapping gravitational lensing of the CMB using local likelihoods
• Gravitational Wave -- Gauge Field Dynamics
• QUIJOTE scientific results -- V. The microwave intensity and polarisation spectra of the Galactic regions W49, W51 and IC443
• Euclid preparation. LIX. Angular power spectra from discrete observations
• Improving Constraints on Inflation with CMB Delensing
• Impact of half-wave plate systematics on the measurement of CMB $B$-mode polarization
• Reassessing Dust's Role in Forming the CMB
• Estimation of spectrum and parameters of relic gravitational waves using space-borne interferometers
• Tensor modes on the string theory landscape
• Compact source detection in multi-channel microwave surveys: from SZ clusters to polarized sources
• Full-sky correlation functions for CMB experiments with asymmetric window functions
• Cross-Correlation Studies with CMB Polarization Maps
• WMAP Polarization Results
• The Annulus-Filtered E and B Modes in CMBR Polarization
• Inflation and CMB Anisotropy from Quantum Metric Fluctuations
• Emergent cosmological constant from colliding electromagnetic waves
• A multifrequency angular power spectrum analysis of the Leiden polarization surveys
• Tensor-induced B modes with no temperature fluctuations
• Extracting parity-violating gravitational waves from projected tidal force tensor in three dimensions
• Cosmic Microwave Background Anisotropy numerical solution (CMBAns) I: An introduction to $C_l$ calculation
• Primordial Gravitational Waves Measurements and Anisotropies of CMB Polarization Rotation
• Impact of intrinsic alignments on clustering constraints of the growth rate
• Cosmology Large Angular Scale Surveyor (CLASS): 90 GHz Telescope Pointing, Beam Profile, Window Function, and Polarization Performance
• Total power horn-coupled 150 GHz LEKID array for space applications
• Constraints on cosmic birefringence using $E$-mode polarisation
• Measuring primordial gravitational waves from CMB B-modes in cosmologies with generalized expansion histories
• Tomographic constraint on anisotropic cosmic birefringence
• Limits on the gravity wave contribution to microwave anisotropies
• On spectral representations of tensor random fields on the sphere
• The Superhorizon Test of Future B-mode Experiments
• Pulsar Timing Residuals Induced by Gravitational Waves from Single Non-evolving Supermassive Black Hole Binaries with Elliptical Orbits
• Using CMB polarization to constrain the anomalous nature of the Cold Spot with an incomplete sky-coverage
• Gravitational waves during inflation in presence of a decaying cosmological parameter from a 5D vacuum theory of gravity
• Observation of gravitational waves by light polarization
• Probabilistic Cosmological Mass Mapping from Weak Lensing Shear
• Non-axisymmetric aberration patterns from wide-field telescopes using spin-weighted Zernike Polynomials
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• Controlling systematics in ground-based CMB surveys with partial boresight rotation
• Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams
• A chemically etched corrugated feedhorn array for D-band CMB observations
• Statistics of non-polarized points in the CMB polarization maps
• A forecast of the sensitivity on the measurement of the optical depth to reionization with the GroundBIRD experiment
• Impact of intrinsic polarisation of Sgr A* historical flares on (polarisation) properties of their X-ray echoes
• The Large-Scale Polarization of the Microwave Foreground
• Topological properties of the Cosmic Microwave Background polarization map
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• Design and characterization of a ground-based absolute polarization calibrator for use with polarization sensitive CMB experiments
• Taller in the saddle: constraining CMB physics using saddle points
• The effect of cosmic variance on the characteristics of dust polarization power spectra
• Isotropic cosmic birefringence from an oscillating axion-like field
• Smoothing methods comparison for CMB E- and B-mode separation
• Atacama Large Aperture Submillimeter Telescope (AtLAST) Science: Resolving the Hot and Ionized Universe through the Sunyaev-Zeldovich effect
• Weak lensing corrections to tSZ-lensing cross correlation
• Prospects for Primordial Gravitational Waves in String Inflation
• Gravitational Lensing of the CMB: a Feynman Diagram Approach
• Optimistic estimation on probing primordial gravitational waves with CMB B-mode polarization
• Imaging parity-violation in the CMB
• Constraining primordial tensor features with the anisotropies of the Cosmic Microwave Background
• QUIJOTE scientific results -- XVIII. New constraints on the polarization of the Anomalous Microwave Emission in bright Galactic regions: $\rho$\,Ophiuchi, Perseus and W43
• Primordial gravitational waves from spontaneous Lorentz symmetry breaking
• The establishment of the Standard Cosmological Model through observations
• Secondary B-mode polarization from Faraday rotation in clusters and galaxies
• The imprint of primordial gravitational waves on the CMB intensity profile
• NP Stokes fields for radio astronomy
• A Pop III generated dust screen at z~16
• Control and systems software for the Cosmology Large Angular Scale Surveyor (CLASS)
• CMB B-mode polarization from Thomson scattering in the local universe
• Genus statistics on CMB polarization maps and cosmological parameters degeneracy
• The two-and three-point correlation functions of the polarized five-year WMAP sky maps
• Cosmic Microwave Background Polarization
• Primordial gravitational waves from the space-condensate inflation model
• Measuring CMB polarisation with the Planck mission
• Predicting the Polarization of The Microwave Background from the WMAP Temperature Maps
• Red Density Perturbations and Inflationary Gravitational Waves
• The Cosmic Microwave Background anisotropies: open problems
• Confronting Inflation Models with the Coming Observations on Primordial Gravitational Waves
• An Upper Limit on the Initial Temperature of the Radiation-Dominated Universe
• Polarizations of CMB and the Hubble tension
• Limits on Polarized Dust Spectral Index Variations for CMB Foreground Analysis
• Optimizing interferometer experiments for CMB B mode measurement
• Smooth $\mu$-Hybrid and Non-Minimal Higgs Inflation in $SU(4{)}_C\times SU(2{)}_L\times SU(2{)}_R$ With Observable Gravitational Waves
• A New Upper Limit on the Polarization of the Cosmic Microwave Background Radiation
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• ForSE+: Simulating non-Gaussian CMB foregrounds at 3 arcminutes in a stochastic way based on a generative adversarial network
• QUIJOTE scientific results -- IX. Radio sources in the QUIJOTE-MFI wide survey maps
• Intermediate and Power-Law Inflation in the Tachyon Model with Constant Sound Speed
• Observable CMB B-modes from Cosmological Phase Transitions
• Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background
• Impact of reionization history on constraining primordial gravitational waves in future all-sky cosmic microwave background experiments
• Reconstruction of full sky CMB $\mathbf{E}$ and $\mathbf{B}$ modes spectra removing $\mathbf{E}$-to-$\mathbf{B}$ leakage from partial sky using deep learning
• Distinguishing Primordial Magnetic Fields from Inflationary Tensor Perturbations in the Cosmic Microwave Background
• Filter Design for the Detection/Estimation of the Modulus of a Vector. Application to Polarization Data
• Barycentric interpolation on Riemannian and semi-Riemannian spaces
• Testing CMB polarization data using position angles
• Weak Gravitational Lensing of CMB - Revisit
• Approximate Likelihood Approaches for Detecting the Influence of Primordial Gravitational Waves in Cosmic Microwave Background Polarization
• An exact result concerning the $1/f$ noise contribution to the large-angle error in CMB temperature and polarization maps
• Imprints of relic gravitational waves on pulsar timing
• On the Scale of Inflation
• Probing pre-inflationary anisotropy with directional variations in the gravitational wave background
• Probing the primordial Universe from the low-multipole CMB data
• Viable Intermediate Inflation in the Mimetic DBI Model
• Tensor Tilt from Primordial B-modes
• CMB delensing with deep learning
• Automatic Nelson-Barr solutions to the strong CP puzzle
• Cosmic Microwave Background anisotropies: the power spectrum and beyond
• Recovery of fluctuation spectrum evolution from tomographic shear spectra
• An "Ultrasonic Image" of the Embryonic Universe: CMB Polarization Tests of the Inflationary Paradigm
• Fisher Matrix Optimization of Cosmic Microwave Background Interferometers
• Robust Likelihoods for Inflationary Gravitational Waves from Maps of Cosmic Microwave Background Polarization
• Testing for directionality in the Planck polarization and lensing data
• Modeling optical systematics for the Taurus CMB experiment
• Perturbation Theory in the Minimally Extended Varying Speed of Light (meVSL) Model
• LiteBIRD science goals and forecasts: improved full-sky reconstruction of the gravitational lensing potential through the combination of Planck and LiteBIRD data
• Parity Violation in Galaxy Shapes: Primordial Non-Gaussianity
• Unbiased Primordial Gravitational Wave Inference from the CMB with SMICA
• KiDS-Legacy: WIMP dark matter constraints from the cross-correlation of weak lensing and Fermi-LAT gamma rays
• Observing low elevation sky and the CMB Cold Spot with BICEP3 at the South Pole
• A quantisation procedure in the presence of an initial Kasner singularity: primordial gravitational waves from triaxially anisotropic pre-inflation
• Primordial Gravitational Waves and Rescattered Electromagnetic Radiation in the Cosmic Microwave Background
• Comparison of the Planck 2018 CMB polarization maps in the BICEP2/Keck region
• Tensor-Induced CMB Temperature-Polarization Correlation in Reionized Universes
• Polarization angle requirements for CMB B-mode experiments. Application to the LiteBIRD satellite
• Reionization process dependence of the ratio of CMB polarization power spectra at low-$\ell$
• An Overview of the SPOrt Experiment
• QUIJOTE-TFGI polarization calibration -- Ground characterization and on-sky validation with Tau A and the Moon
• Primordial observables of explicit diffeomorphism violation in gravity
• Time-dependent deflection reconstruction: new technique to search for gravitational waves with the cosmic microwave background
• Dipole Modulation in Tensor Modes: Signatures in CMB Polarization
• Generation of CMB B-mode Polarization from Circular Polarization
• CMB Observational Techniques and Recent Results
• The CMB Cold Spot under the lens II: Lensing signatures in polarization and cosmic texture footprints
• Accurate and efficient likelihood modeling for large-scale CMB data
• Zero-polarization candidate regions for calibration of wide-field optical polarimeters
• Systematic error cancellation for a four-port interferometric polarimeter
• Secondary CMB anisotropies from magnetized halos --I: Power spectra of the Faraday rotation angle and conversion rate
• Weighting CMB and Galactic synchrotron polarisation
• Pulsar timing residuals due to individual non-evolving gravitational wave sources
• Adaptive Nonparametric Regression on Spin Fiber Bundles