Krause, E. and Hirata, C. M. (2010) Weak lensing power spectra for precision cosmology : Multipledeflection, reduced shear, and lensing bias corrections. Astronomy and Astrophysics, 523 . Art. No. A28. ISSN 00046361. http://resolver.caltech.edu/CaltechAUTHORS:20110118142202538

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Abstract
It is usually assumed that the ellipticity power spectrum measured in weak lensing observations can be expressed as an integral over the underlying matter power spectrum. This is true at order O(Φ^2) in the gravitational potential. We extend the standard calculation, constructing all corrections to order O(Φ^4). There are four types of corrections: corrections to the lensing shear due to multipledeflections; corrections due to the fact that shape distortions probe the reduced shear γ/(1 − κ) rather than the shear itself; corrections associated with the nonlinear conversion of reduced shear to mean ellipticity; and corrections due to the fact that observational galaxy selection and shear measurement is based on galaxy brightnesses and sizes which have been (de)magnified by lensing. We show how the previously considered corrections to the shear power spectrum correspond to terms in our analysis, and highlight new terms that were not previously identified. All correction terms are given explicitly as integrals over the matter power spectrum, bispectrum, and trispectrum, and are numerically evaluated for the case of sources at z = 1. We find agreement with previous works for the O(Φ^3) terms. We find that for ambitious future surveys, the O(Φ^4) terms affect the power spectrum at the ~1−5σ level; they will thus need to be accounted for, but are unlikely to represent a serious difficulty for weak lensing as a cosmological probe.
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Additional Information:  © 2010 ESO. Received 22 October 2009, Accepted 11 August 2010, Published online 15 November 2010. E.K. and C.H. are supported by the US National Science Foundation under AST0807337 and the US Department of Energy under DEFG03 02ER40701. C.H. is supported by the Alfred P. Sloan Foundation. We thank Wayne Hu, Fabian Schmidt, Peter Schneider and Chaz Shapiro for useful discussions.  
Group:  TAPIR  
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Subject Keywords:  cosmology: theory – gravitational lensing: weak – largescale structure of the Universe – methods: analytical  
Record Number:  CaltechAUTHORS:20110118142202538  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20110118142202538  
Official Citation:  Weak lensing power spectra for precision cosmology  Multipledeflection, reduced shear, and lensing bias corrections E. Krause and C. M. Hirata A&A 523 A28 (2010) DOI: 10.1051/00046361/200913524  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  21797  
Collection:  CaltechAUTHORS  
Deposited By:  Benjamin Perez  
Deposited On:  18 Jan 2011 23:41  
Last Modified:  26 Dec 2012 12:51 
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