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 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. Combining the lensing effect for lenses at three
different redshifts and three different source redshifts, a relation between
shear ratios is derived which 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.
