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Cosmic shear is a powerful method to constrain cosmology, provided that anysystematic effects are under control. The intrinsic alignment of galaxies isexpected to severely bias parameter estimates if not taken into account. Weexplore the potential of a joint analysis of tomographic galaxy ellipticity,galaxy number density, and ellipticity-number density cross-correlations tosimultaneously constrain cosmology and self-calibrate unknown intrinsicalignment and galaxy bias contributions. We treat intrinsic alignments andgalaxy biasing as free functions of scale and redshift and marginalise over theresulting parameter sets. Constraints on cosmology are calculated by combiningthe likelihoods from all two-point correlations between galaxy ellipticity andgalaxy number density. The information required for these calculations isalready available in a standard cosmic shear dataset. We include contributionsto these functions from cosmic shear, intrinsic alignments, galaxy clusteringand magnification effects. In a Fisher matrix analysis we compare ourconstraints with those from cosmic shear alone in the absence of intrinsicalignments. For a potential future large area survey, such as Euclid, the extrainformation from the additional correlation functions can make up for theadditional free parameters in the intrinsic alignment and galaxy bias terms,depending on the flexibility in the models. For example, the Dark Energy TaskForce figure of merit is recovered even when more than 100 free parameters aremarginalised over. We find that the redshift quality requirements are similarto those calculated in the absence of intrinsic alignments.

Simultaneous measurement of cosmology and intrinsic alignments using joint cosmic shear and galaxy number density correlations