Shear Ratio Tests: Cancelling Growth to Isolate the Geometry of the Lensing Signal

Tangential shear measured around the same foreground lenses for two different source populations has a ratio set almost entirely by geometry, because the mass distribution responsible is common to both measurements. This paper computes the geometric factor for a lens plane at redshift 0.35 and source planes from redshift 0.6 to 1.6, and the ratio between the factors for sources at redshifts 1.2 and 0.6, which is 1.685. For sources at redshift 0.9 the geometric factor is 0.548. The derivative of the ratio with respect to the matter density is -0.146 per unit change, confirming that the ratio is a weak but clean geometric probe: it constrains distances and source redshift distributions while being, by construction, blind to the growth of structure and hence to most early-universe physics. All quantities are computed from stated assumptions, not measured.