Cross-Correlation of spectroscopic and photometric galaxy surveys:
  cosmology from lensing and redshift distortions
  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.
