Generalized shear-ratio tests: A new relation between cosmological distances, and a diagnostic for a redshift-dependent multiplicative bias in shear measurements

We derive a new relation between cosmological distances that is valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields an equation between those distance ratios that are the geometrical factors determining the strength of the gravitational lensing effect of mass concentrations. Considering a combination of weak-lensing shear ratios, based on lenses at two different redshifts and sources at three different redshifts, we derive a relation between shear-ratio tests that must be identically satisfied. A redshift-dependent multiplicative bias in shear estimates will violate this relation, and thus can be probed by this generalized shear-ratio test. Combining the lensing effect for lenses at three different redshifts and three different source redshifts, a relation between shear ratios is derived that must be valid independent of a multiplicative bias. We propose these generalized shear-ratio tests as a diagnostic for the presence of systematics in upcoming weak-lensing surveys.