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The weak gravitational lensing of distant galaxies by large-scale structureis expected to become a powerful probe of dark energy. By measuring theellipticities of large numbers of background galaxies, the subtle gravitationaldistortion called "cosmic shear" can be measured and used to constrain darkenergy parameters. The observed galaxy ellipticities, however, are induced notby shear but by reduced shear, which also accounts for slight magnifications ofthe images. This distinction is negligible for present weak lensing surveys,but it will become more important as we improve our ability to measure andunderstand small-angle cosmic shear modes. I calculate the discrepancy betweenshear and reduced shear in the context of power spectra and cross spectra,finding the difference could be as high as 10% on the smallest accessibleangular scales. I estimate how this difference will bias dark energy parametersobtained from two weak lensing methods: weak lensing tomography and the shearratio method known as offset-linear scaling. For weak lensing tomography,ignoring the effects of reduced shear will cause future surveys considered bythe Dark Energy Task Force to measure dark energy parameters that are biased byamounts comparable to their error bars. I advocate that reduced shear beproperly accounted for in such surveys, and I provide a semi-analytic formulafor doing so. Since reduced shear cross spectra do not follow an offset-linearscaling relation, the shear ratio method is similarly biased but with smallersignificance.

Biased Dark Energy Constraints from Neglecting Reduced Shear in Weak Lensing Surveys