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Gravitational lensing of the CMB: A Feynman diagram approach

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We develop a Feynman diagram approach to calculating correlations of the Cosmic Microwave Background (CMB) in the presence of distortions. As one application, we focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). We study the Hu-Okamoto quadratic estimator for extracting lensing from the CMB and derive the noise of the estimator up to O(φ4) in the lensing potential φ. By identifying the diagrams responsible for the previously noted large O(φ4) term, we conclude that the lensing expansion does not break down. The convergence can be significantly improved by a reorganization of the φ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel, including many previously unexplored cases. We briefly discuss other applications to cosmology of this diagrammatic approach, such as distortions of the CMB due to patchy reionization, or due to Faraday rotation from primordial axion fields. © 2014.

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