Cosmological galaxy surveys aim at mapping the largest volumes to test models with techniques such as cluster abundance, cosmic shear correlations or baryon acoustic oscillations (BAO), which are designed to be independent of galaxy bias. Here we explore an alternative route to constrain cosmology: sampling more moderate volumes with the cross-correlation of photometric and spectroscopic surveys. We consider the angular galaxy-galaxy autocorrelation in narrow redshift bins and its combination with different probes of weak gravitational lensing (WL) and redshift space distortions (RSD). Including the cross-correlation of these surveys improves by factors of a few the constraints on both the dark energy equation of state w(z) and the cosmic growth history, parametrized by gamma. The additional information comes from using many narrow redshift bins and from galaxy bias, which is measured both with WL probes and RSD, breaking degeneracies that are present when using each method separately. We show forecasts for a joint w(z) and gamma figure of merit using linear scales over a deep (i<24) photometric survey and a brighter (i<22.5) spectroscopic or very accurate (0.3%) photometric redshift survey. Magnification or shear in the photometric sample produce FoM that are of the same order of magnitude of those of RSD or BAO over the spectroscopic sample. However, the cross-correlation of these probes over the same area yields a FoM that is up to a factor 100 times larger. Magnification alone, without shape measurements, can also be used for these cross-correlations and can produce better results than using shear alone. For a spectroscopic follow-up survey strategy, measuring the spectra of the foreground lenses to perform this cross-correlation provides 5 times better FoM than targeting the higher redshift tail of the galaxy distribution to study BAO over a 2.5 times larger volume.
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