A weak lensing detection of the cosmological distance-redshift relation behind three massive clusters

The amplitude of weak lensing should increase with source distance, rising steeply behind a lens and saturating at high redshift, providing a model-independent means of measuring cosmic geometry. We measure the amplitude of weak lensing with redshift for three massive clusters, A370 (z= 0.375), ZwCl0024+17 (z= 0.395) and RXJ1347−11 (z= 0.451), using deep, three-colour Subaru imaging. We define the depth of lensed populations with reference to the COSMOS and GOODS fields, providing a consistency check of photo-z estimates over a wide range of redshift and magnitude. The predicted distance-redshift relation is followed well for the deepest data set, A370, for a wide range of cosmologies, and is consistent with less accurate data for the other two clusters. Scaling this result to a new survey of ∼25 massive clusters should provide a useful cosmological constraint on w, complementing existing techniques, with distance measurements covering the untested redshift range, 1 < z < 5.