Gravitational Lensing of the CMB: a Feynman Diagram Approach

Abstract

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 $\mathcal{O}({\varphi }^4)$ in the lensing potential $\varphi$. The previously noted large $\mathcal{O}({\varphi }^4)$ term can be significantly reduced by a reorganization of the $\varphi$ expansion. Our approach makes it simple to obtain expressions for quadratic estimators based on any CMB channel. 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.

5 pages, 8 figures, v2: journal version

References in corpus (7)

• CMBPol Mission Concept Study: Probing Inflation with CMB Polarization
• CMB temperature lensing power reconstruction
• Reconstructing Patchy Reionization from the Cosmic Microwave Background
• Pseudoscalar perturbations and polarization of the cosmic microwave background
• How to De-Rotate the Cosmic Microwave Background Polarization
• De-Rotation of the Cosmic Microwave Background Polarization: Full-Sky Formalism
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Cited by in corpus (2)

• The reconstructed CMB lensing bispectrum
• CMB lensing power spectrum without noise bias