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With the wealth of forthcoming data from wide-field surveys, it is more important than ever to understand the full range of independent probes of cosmology at our disposal. Here, we explore the potential for galaxy clustering and cosmic shear, separately and in combination, including the effects of lensing magnification. We show that inferred cosmological parameters may be biased when flux magnification is neglected. Results are presented for Stage III ground-based and Stage IV space-based photometric surveys, using slopes of the luminosity function inferred from the Canada-France-Hawaii Lensing Survey catalogue. We find that combining with clustering improves the shear Dark Energy Task Force-like Figure of Merit by a factor of 1.33 using only autocorrelations in redshift for the clustering analysis, rising to 1.52 when cross-correlations are also included. The further addition of galaxy-galaxy lensing gives increases in the shear Figure of Merit by a factor of 2.82 and 3.7 for each type of clustering analysis, respectively. The presence of flux magnification in a clustering analysis does not significantly affect the precision of cosmological constraints when combined with cosmic shear and galaxy-galaxy lensing. However, if magnification is neglected, inferred cosmological parameter values are biased, with biases in some cosmological parameters larger than statistical errors.
Duncan et al. (Tue,) studied this question.