The Effects of Neglecting Reduced Shear on Dark Energy Constraints from Three-dimensional Weak Lensing Methods

The weak gravitational lensing of distant galaxies by large-scale structure is expected to become a powerful probe of dark energy. By measuring the ellipticities of large numbers of background galaxies, the subtle gravitational distortion called "cosmic shear" can be measured and used to constrain dark energy parameters. The observed galaxy ellipticities, however, are induced not by shear but by reduced shear, which also accounts for slight magnifications of the images. This distinction is negligible for present weak lensing surveys, but it will become more important as we improve our ability to measure and understand small-angle cosmic shear modes. I calculate the discrepancy between shear and reduced shear in the context of power spectra and cross spectra, finding the difference could be as high as 10% on the smallest accessible angular scales. I estimate how this difference will bias dark energy parameters obtained from two types of 3D weak lensing methods: weak lensing tomography and the shear ratio method known as offset-linear scaling. For weak lensing tomography, ignoring the effects of reduced shear will cause future surveys such as the Dark Energy Survey, Large Synoptic Survey Telescope, or Joint Dark Energy Mission to bias their dark energy parameters by amounts that are comparable to their error bars. I advocate that reduced shear be properly accounted for in these surveys, and I provide a semi-analytic formula for doing so. For a space telescope such as the Joint Dark Energy Mission, the offset-linear scaling method is insensitive to reduced shear for modes l ≤ 3000, but the method becomes invalid when including modes with l ≥ 5000. Reduced shear could have important consequences for other observables such as the weak lensing of the cosmic microwave background.