Dark energy constraints from weak-lensing cross-correlation cosmography

We present a method for implementing the idea of Jain & Taylor for constraining cosmological parameters with weak gravitational lensing. Photometric redshift information on foreground galaxies is used to produce templates of the mass structure at foreground slices z(l), and the predicted distortion field is cross-correlated with the measured shapes of sources at redshift z(s). The variation of the cross-correlation with z(s) depends purely on ratios of angular diameter distances. We propose a formalism for such an analysis that makes use of all foreground-background redshift pairs and derive the Fisher uncertainties on the dark energy parameters that would result from such a survey. Surveys from the proposed Supernova/Acceleration Probe ( SNAP) satellite or the Large Synoptic Survey Telescope (LSST) observatory could constrain the dark energy equation of state to sigma(w0) approximate to 0.01f(sky)(-1/2) and sigma(wa) approximate to0.035f(sky)(-1/2) after application of a practical prior on Omega(m). Advantages of this method over power-spectrum measurements are that it is unaffected by residual point-spread function distortions, is not limited by sample variance, and can use nonlinear mass structures to constrain the cosmology. The signal is, however, very small, amounting to a change of a few parts in 10(3) of the lensing distortion. In order to realize the full sensitivity to cosmological parameters, the calibration of lensing distortion must be independent of redshift to comparable levels, and photometric redshifts must be similarly free of bias. Both of these tasks require substantial advances over the present state of the art, but we discuss how such accurate calibrations might be achieved using internal consistency tests. Elimination of redshift bias would require the spectroscopic redshifts of similar to10(4)-10(5) high-redshift galaxies - fewer for lensing surveys less ambitious than SNAP or LSST.