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 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.
Highlights
Primary anisotropies in the Cosmic Microwave Background (CMB) were generated around 375,000 years after the “big bang,” when the universe was still in the linear regime
During the photon’s journey to us, it encounters several distorting fields, which make the CMB non-Gaussian and statistically anisotropic. Examples of such distorting fields are (a) gravitational lensing which bends the light as photons travel though the Large Scale Structure (LSS) [6,7,8,9], (b) patchy reionization which modulates the CMB intensity because of scattering when Hydrogen reionizes [10], and (c) cosmological rotation, due to parity-violating physics, which rotates the plane of polarization of the CMB [11,12,13,14]
We show that the previously unexplained large N(2) noise can be understood from the contributing diagrams, and reduced by reorganizing the expansion
Summary
A Department of Physics, University of California at San Diego, La Jolla, CA 92093, USA b Nikhef, Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands c ITFA, University of Amsterdam, Science Park 904, 1018 XE, Amsterdam, The Netherlands article info. Article history: Received 30 June 2014 Accepted 1 July 2014 Available online 5 July 2014 Editor: B. We focus on CMB distortions due to gravitational lensing by Large Scale Structure (LSS). 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
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