Lensing of the CMB: Non Gaussian aspects

Abstract

We study the generation of CMB anisotropies by gravitational lensing on small angular scales. We show these fluctuations are not Gaussian. We prove that the power spectrum of the tail of the CMB anisotropies on small angular scales directly gives the power spectrum of the deflection angle. We show that the generated power on small scales is correlated with the large scale gradient. The cross correlation between large scale gradient and small scale power can be used to test the hypothesis that the extra power is indeed generated by lensing. We compute the three and four point function of the temperature in the small angle limit. We relate the non-Gaussian aspects presented in this paper as well as those in our previous studies of the lensing effects on large scales to the three and four point functions. We interpret the statistics proposed in terms of different configurations of the four point function and show how they relate to the statistic that maximizes the S/N.

Changes to match accepted version in PRD, 20 pages 10 figures. Better resolution images of the figures can be found at http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.html

References in corpus (1)

• Foregrounds and Forecasts for the Cosmic Microwave Background

Cited by in corpus (86)

• Non-Gaussianity from Inflation: Theory and Observations
• Weak Gravitational Lensing of the CMB
• Cosmic Microwave Background Anisotropies
• Reconstruction of lensing from the cosmic microwave background polarization
• Cosmology with Weak Lensing Surveys
• A measurement of gravitational lensing of the microwave background using South Pole Telescope data
• CMB lensing from Planck PR4 maps
• The Angular Trispectrum of the CMB
• Gravitational lensing as a contaminant of the gravity wave signal in CMB
• Dark Synergy: Gravitational Lensing and the CMB
• Correlation of CMB with large-scale structure: II. Weak lensing
• Mapping the Dark Matter through the CMB Damping Tail
• The shape of the CMB lensing bispectrum
• Lensing Reconstruction with CMB Temperature and Polarization
• The Angular Trispectra of CMB Temperature and Polarization
• Analyzing weak lensing of the cosmic microwave background using the likelihood function
• CMB temperature lensing power reconstruction
• Primordial Bispectrum Information from CMB Polarization
• Impact of post-Born lensing on the CMB
• Reconstructing Patchy Reionization from the Cosmic Microwave Background
• Optimal Estimation of Non-Gaussianity
• Weak lensing of the CMB
• Cosmological Information from Lensed CMB Power Spectra
• Evidence of Lensing of the Cosmic Microwave Background by Dark Matter Halos
• Secondary anisotropies of the CMB
• Numerical study of statistical properties of the lensing excursion angles
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Cross-correlation of CMB with large-scale structure: weak gravitational lensing
• Cluster Mass Estimators from CMB Temperature and Polarization Lensing
• The Far-Infrared Background Correlation with CMB Lensing
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• Exploring cosmic origins with CORE: gravitational lensing of the CMB
• Non-Gaussian Aspects of Thermal and Kinetic Sunyaev-Zel'dovich Effects
• Principal Power of the CMB
• Compensated Isocurvature Perturbations and the Cosmic Microwave Background
• Simulation of non-Gaussian CMB maps
• CMB Temperature and Polarization Anisotropy Fundamentals
• The Benefits of CMB Delensing
• The Weak Lensing Bispectrum
• Beyond the Damping Tail: Cross-Correlating the Kinetic Sunyaev-Zel'dovich Effect with Cosmic Shear
• A Large Sky Simulation of the Gravitational Lensing of the Cosmic Microwave Background
• The full squeezed CMB bispectrum from inflation
• Tensions between direct measurements of the lens power spectrum from Planck data
• CMB Lensing Reconstruction in Real Space
• What can be learned from the lensed cosmic microwave background B-mode polarization power spectrum?
• Weak Lensing of the CMB by Large-Scale Structure
• Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation
• Cluster Masses from CMB and Galaxy Weak Lensing
• CMB-Cluster Lensing
• Baryon history and cosmic star formation in non-Gaussian cosmological models: numerical simulations
• CMB B-polarization to map the Large-scale Structures of the Universe
• Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel'dovich effect
• The Intrinsic Matter Bispectrum in $\Lambda$CDM
• Counts of high-redshift GRBs as probe of primordial non-Gaussianities
• Minimizing gravitational lensing contributions to the primordial bispectrum covariance
• CMB lensing and primordial squeezed non-Gaussianity
• Weak Lensing of the CMB: Cumulants of the Probability Distribution Function
• Weak Lensing of the Primary CMB Bispectrum
• A Constraint On the Integrated Mass Power Spectrum out to z = 1100 from Lensing of the Cosmic Microwave Background
• Weak Gravitational Lensing of High-Redshift 21 cm Power Spectra
• Weak Lensing of the CMB: Power Spectrum Covariance
• Intervening Mg II absorption systems from the SDSS DR12 quasar spectra
• The imprint of cosmological non-Gaussianities on primordial structure formation
• Real space estimator for the weak lensing convergence from the CMB
• CMB Lens Sample Covariance and Consistency Relations
• Real space lensing reconstruction using cosmic microwave background polarization
• Impact of Instrumental Systematic Contamination on the Lensing Mass Reconstruction using the CMB Polarization
• Detectability of Gravitational Lensing Effect on the Two-point Correlation Function of Hotspots in the CMB maps
• The Impact of Secondary non-Gaussianities in the CMB on Cosmological Parameter Estimation
• Statistics of the Sunyaev-Zel'dovich Effect power spectrum
• Improving Constraints on Inflation with CMB Delensing
• Probing inflation with CMB polarization : weak lensing effect on the covariance of CMB spectra
• Applications of High Resolution High Sensitivity Observations of the CMB
• Higher-Order Gravitational Lensing Reconstruction using Feynman Diagrams
• A test of the Suyama-Yamaguchi inequality from weak lensing
• Lensing-induced Non-Gaussian Signatures in the Cosmic Microwave Background
• Weak lensing of the Sunyaev-Zel'dovich sky
• A Simple Gravitational Lens Model For Cosmic Voids
• Gravitational Lensing of the CMB: a Feynman Diagram Approach
• Hydrodynamical chemistry simulations of the SZ effect and the impacts from primordial non-Gaussianities
• Simulations and Observations of the Microwave Universe
• Small Correlated Against Large Estimator (SCALE) for Cosmic Microwave Background Lensing
• On the Cross-Correlation between Dark Matter Distribution and Secondary CMB Anisotropies by Ionized Intergalactic Medium
• The shape of high order correlation functions in CMB anisotropy maps
• A Small-Scale Modification to the Lensing Kernel
• Running the small-correlated-against-large estimator at scale: Applications of small-scale CMB lensing estimators on realistic simulations