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We develop a new method of combining cluster observables (number counts and cluster-cluster correlation functions) and stacked weak lensing signals of background galaxy shapes, both of which are available in a wide-field optical imaging survey. Assuming that the clusters have secure redshift estimates, we show that the joint experiment enables a self-calibration of important systematic errors inherent in these measurements, including the source redshift uncertainty and the cluster mass-observable relation, by adopting a single population of background source galaxies for the lensing analysis. The single source galaxy population allows us to use the relative strengths of the stacked lensing signals at different cluster redshifts for calibrating the source redshift uncertainty, which in turn leads to accurate measurements of the mean cluster mass in each redshift and mass bin. In addition, our formulation of the stacked lensing signals in Fourier space simplifies the Fisher matrix calculations, as well as the marginalization over the cluster off-centering effect which is one of the most significant uncertainties in the stacked lensing analysis. We show that upcoming wide-field surveys covering more than a few thousand square degrees yield stringent constraints on cosmological parameters including dark energy parameters, without any priors on nuisance parameters that model systematic uncertainties. Specifically, the stacked lensing information improves the dark energy figure of merit by a factor of 4, compared to that from the cluster observables alone. The primordial non-Gaussianity parameter can also be constrained with a level of (f₍₋) 10. In this method, the mean source redshift is well calibrated to an accuracy of 0. 1 in redshift, and the mean cluster mass in each bin to 5--10% accuracies, which demonstrates the success of the self-calibration of systematic uncertainties from the joint experiment.
Oguri et al. (Tue,) studied this question.