Weak lensing of the CMB: extraction of lensing information from the trispectrum |
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| Institution: | 1. Multidisciplinary Center for Infrastructure Engineering, Shenyang University of Technology, Shenyang 110870, China;2. School of Civil Engineering, Shandong Jianzhu University, Jinan 250101, China;3. Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089-2531, USA;4. Department of Civil Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada;1. Business School, Sichuan University, Chengdu, 610064, PR China;2. Institute of New Energy and Low-Carbon Technology, Sichuan University, Chengdu, 610064, PR China;1. College of Food Science and Technology, Huazhong Agricultural University, Wuhan, 430070, China;2. Key Laboratory of Fermentation Engineering, Ministry of Education, National “111” Center for Cellular Regulation and Molecular Pharmaceutics, Hubei Key Laboratory of Industrial Microbiology, School of Biological Engineering and Food, Hubei University of Technology, Wuhan, 430068, China;3. Key Laboratory of Environment Correlative Dietology (Huazhong Agricultural University), Ministry of Education, China;4. Functional Food Engineering & Technology Research Center of Hubei Province, China;5. College of Life Sciences, South-Central Minzu University, Wuhan, China;1. Civil, Construction and Environmental Engineering, Iowa State University, Ames, IA, USA;2. Department of Building Technology, Linnaeus University, Sweden;3. Department of Electrical Engineering, Qatar University, Qatar;4. Department of Civil Engineering, Qatar University, Qatar;5. Department of Signal Processing, Tampere University of Technology, Finland;6. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA;1. Department of Financial Engineering, University of Science & Culture, Tehran, Iran;2. Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran |
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| Abstract: | We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities. |
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