# Higher-order gravitational lensing reconstruction using Feynman diagrams

## Abstract

We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O (φ{sup 4}) in the lensing potential φ. We consider both the diagonal noise TT TT, EB EB, etc. and, for the first time, the off-diagonal noise TT TE, TB EB, etc. The previously noted large O (φ{sup 4}) term in the second order noise is identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the φ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one B component of the CMB, such as EE EB.

- Authors:

- Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States)
- Nikhef, Theory Group, Science Park 105, 1098 XG, Amsterdam (Netherlands)

- Publication Date:

- OSTI Identifier:
- 22375883

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; FARADAY EFFECT; FEYNMAN DIAGRAM; GRAVITATIONAL LENSES; NOISE; POTENTIALS; RELICT RADIATION; SPECTRA

### Citation Formats

```
Jenkins, Elizabeth E., Manohar, Aneesh V., Yadav, Amit P.S., and Waalewijn, Wouter J., E-mail: ejenkins@ucsd.edu, E-mail: amanohar@ucsd.edu, E-mail: W.J.Waalewijn@uva.nl, E-mail: ayadav@physics.ucsd.edu.
```*Higher-order gravitational lensing reconstruction using Feynman diagrams*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/024.

```
Jenkins, Elizabeth E., Manohar, Aneesh V., Yadav, Amit P.S., & Waalewijn, Wouter J., E-mail: ejenkins@ucsd.edu, E-mail: amanohar@ucsd.edu, E-mail: W.J.Waalewijn@uva.nl, E-mail: ayadav@physics.ucsd.edu.
```*Higher-order gravitational lensing reconstruction using Feynman diagrams*. United States. doi:10.1088/1475-7516/2014/09/024.

```
Jenkins, Elizabeth E., Manohar, Aneesh V., Yadav, Amit P.S., and Waalewijn, Wouter J., E-mail: ejenkins@ucsd.edu, E-mail: amanohar@ucsd.edu, E-mail: W.J.Waalewijn@uva.nl, E-mail: ayadav@physics.ucsd.edu. Mon .
"Higher-order gravitational lensing reconstruction using Feynman diagrams". United States.
doi:10.1088/1475-7516/2014/09/024.
```

```
@article{osti_22375883,
```

title = {Higher-order gravitational lensing reconstruction using Feynman diagrams},

author = {Jenkins, Elizabeth E. and Manohar, Aneesh V. and Yadav, Amit P.S. and Waalewijn, Wouter J., E-mail: ejenkins@ucsd.edu, E-mail: amanohar@ucsd.edu, E-mail: W.J.Waalewijn@uva.nl, E-mail: ayadav@physics.ucsd.edu},

abstractNote = {We develop a method for calculating the correlation structure of the Cosmic Microwave Background (CMB) using Feynman diagrams, when the CMB has been modified by gravitational lensing, Faraday rotation, patchy reionization, or other distorting effects. This method is used to calculate the bias of the Hu-Okamoto quadratic estimator in reconstructing the lensing power spectrum up to O (φ{sup 4}) in the lensing potential φ. We consider both the diagonal noise TT TT, EB EB, etc. and, for the first time, the off-diagonal noise TT TE, TB EB, etc. The previously noted large O (φ{sup 4}) term in the second order noise is identified to come from a particular class of diagrams. It can be significantly reduced by a reorganization of the φ expansion. These improved estimators have almost no bias for the off-diagonal case involving only one B component of the CMB, such as EE EB.},

doi = {10.1088/1475-7516/2014/09/024},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}