Dark Energy Constraints from Weak‐Lensing Cross‐Correlation Cosmography

We present a method to implement the idea of Jain & Taylor to constraincosmological parameters with weak gravitational lensing. Photometric redshiftinformation on foreground galaxies is used to produce templates of the massstructure at foreground slices z_\ell, and the predicted distortion field iscross-correlated with the measured shapes of sources at redshift z_s. Thevariation of the cross-correlation with z_s depends purely on ratios of angulardiameter distances. We propose a formalism for such an analysis that makes useof all foreground-background redshift pairs, and derive the Fisheruncertainties on the dark energy parameters that would result from such asurvey. Surveys from the proposed SNAP satellite or the LSST observatory couldconstrain the dark energy equation of state to 0.01 f_sky^{-1/2} in w_0 and0.035 f_sky^{-1/2} in w_a after application of a practical prior on \Omega_m.Advantages of this method over power-spectrum measurements are that it isunaffected by residual PSF distortions, is not limited by sample-variance, andcan use non-linear mass structures to constrain cosmology. The signal is,however, very small, amounting to a change of a few parts in 10^3 of thelensing distortion. The calibration of lensing distortion must be independentof redshift to comparable levels, and photometric redshifts must be similarlyfree of bias. Both of these tasks require substantial advance over the presentstate of the art, but we discuss how such accurate calibrations might beachieved using internal consistency tests. Elimination of redshift bias wouldrequire spectroscopic redshifts of 10^4-10^5 high redshift galaxies.Comment: 10 pages, uses emulateapj.cls. Accepted to Ap