Localizing Transformations of the Galaxy-Galaxy Lensing Observable

Abstract: Modern cosmological analyses of galaxy-galaxy lensing face a theoretical systematic effect arising from the non-locality of the observed galaxy-galaxy lensing signal. Because the predicted tangential shear signal at a given separation depends on the physical modeling on all scales internal to that separation, systematic uncertainties in the modeling of non-linear small scales are propagated outwards to larger scales. Even in the absence of other limiting factors, this systematic effect alone can necessitate conservative small-scale cuts, resulting in significant losses of information in the tangential shear data vector. We construct a simple linear transformation of the observable that removes this non-locality, enabling more aggressive small-scale cuts for a given theoretical model. Our modified galaxy-galaxy lensing observable makes it possible to include observations on significantly smaller scales than those under the standard approach in cosmological analyses. More importantly, it ensures that the cosmological signal contained within the observable is exclusively drawn from well-understood physical scales.