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

Understand

We derive a new relation between cosological distances, 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 which 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 which 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.