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Analyzing weak lensing of the cosmic microwave background using the likelihood function

Hirata, Christopher M. and Seljak, Uroš (2003) Analyzing weak lensing of the cosmic microwave background using the likelihood function. Physical Review D, 67 (4). Art. No. 043001. ISSN 2470-0010. doi:10.1103/PhysRevD.67.043001.

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Future experiments will produce high-resolution temperature maps of the cosmic microwave background (CMB) and are expected to reveal the signature of gravitational lensing by intervening large-scale structures. We construct all-sky maximum-likelihood estimators that use the lensing effect to estimate the projected density (convergence) of these structures, its power spectrum, and cross-correlation with other observables. This contrasts with earlier quadratic-estimator approaches that Taylor expanded the observed CMB temperature to linear order in the lensing deflection angle; these approaches gave estimators for the temperature-convergence correlation in terms of the CMB three-point correlation function and for the convergence power spectrum in terms of the CMB four-point correlation function, which can be biased and nonoptimal due to terms beyond the linear order. We show that for sufficiently weak lensing, the maximum-likelihood estimator reduces to the computationally less demanding quadratic estimator. The maximum likelihood and quadratic approaches are compared by evaluating the root-mean-square (rms) error and bias in the reconstructed convergence map in a numerical simulation; it is found that both the rms errors and bias are of order 1 percent for the case of Planck and of order 10–20 percent for a 1 arcminute beam experiment. We conclude that for recovering lensing information from temperature data acquired by these experiments, the quadratic estimator is close to optimal, but further work will be required to determine whether this is also the case for lensing of the CMB polarization field.

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Hirata, Christopher M.0000-0002-2951-4932
Additional Information:©2003 The American Physical Society. Received 24 September 2002; published 12 February 2003. The authors wish to thank Matias Zaldarriaga, Nikhil Padmanabhan, Lyman Page and Vassilios Papathanakos for useful comments and help. C.H. was supported through the NASA Graduate Student Researchers Program, Grant No. NASA GSRP-02-OSS-079. U.S. was supported by NASA ATP and LTSA grants, NSF CAREER grant and grants from David and Lucille Packard Foundation and Alfred P. Sloan Foundation.
Funding AgencyGrant Number
NASA Graduate Student Research FellowshipGSRP-02-OSS-079
David and Lucile Packard FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:HIRprd03a
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ID Code:11092
Deposited By: Archive Administrator
Deposited On:14 Jul 2008 21:11
Last Modified:08 Nov 2021 21:32

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