Weak Lensing of the CMB: Power Spectrum Covariance

Abstract

We discuss the non-Gaussian contribution to the power spectrum covariance of cosmic microwave background (CMB) anisotropies resulting through weak gravitational lensing angular deflections and the correlation of deflections with secondary sources of temperature fluctuations generated by the large scale structure, such as the integrated Sachs-Wolfe effect and the Sunyave-Zel'dovich effect. This additional contribution to the covariance of binned angular power spectrum, beyond the well known cosmic variance and any associated instrumental noise, results from a trispectrum, or a four point correlation function, in temperature anisotropy data. With substantially wide bins in multipole space, the resulting non-Gaussian contribution from lensing to the binned power spectrum variance is insignificant out to multipoles of a few thousand and is not likely to affect the cosmological parameter estimation through acoustic peaks and the damping tail. The non-Gaussian contribution to covariance, however, should be considered when interpreting binned CMB power spectrum measurements at multipoles of a few thousand corresponding to angular scales of few arcminutes and less.

10 pages, 5 figures; submitted to Phys. Rev. D

References in corpus (4)

• The Angular Trispectrum of the CMB
• Power Spectrum Covariance of Weak Gravitational Lensing
• Non-Gaussian Aspects of Thermal and Kinetic Sunyaev-Zel'dovich Effects
• Squared temperature-temperature power spectrum as a probe of the CMB bispectrum

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• CMB Lensing Reconstruction in Real Space
• Weak Lensing of the CMB: Cumulants of the Probability Distribution Function
• Non-Gaussian Covariance of CMB B-modes of Polarization and Parameter Degradation
• Impact of Point Source Clustering on Cosmological Parameters with CMB Anisotropies
• Real space estimator for the weak lensing convergence from the CMB
• Lensing-induced morphology changes in CMB temperature maps in modified gravity theories
• Impact of Instrumental Systematic Contamination on the Lensing Mass Reconstruction using the CMB Polarization
• The Impact of Secondary non-Gaussianities in the CMB on Cosmological Parameter Estimation
• Probing inflation with CMB polarization : weak lensing effect on the covariance of CMB spectra