Combining Spectroscopic and Photometric Surveys: Same or different sky?
  This article looks at the combined constraints from a photometric and
spectroscopic survey. These surveys will measure cosmology using weak lensing
(WL), galaxy clustering, baryon acoustic oscillations (BAO) and redshift space
distortions (RSD). We find, contrary to some findings in the recent literature,
that overlapping surveys can give important benefits when measuring dark
energy. We therefore try to clarify the status of this issue with a full
forecast of two stage-IV surveys using a new approach to properly account for
covariance between the different probes in the overlapping samples. The benefit
of the overlapping survey can be traced back to two factors: additional
observables and sample variance cancellation. Both needs to be taken into
account and contribute equally when combining 3D power spectrum and 2D
correlations for lensing. With an analytic example we also illustrate that for
optimal constraints, one should minimize the (Pearson) correlation coefficient
between cosmological and nuisance parameters and maximize the one among
nuisance parameters (e.g. galaxy bias) in the two samples. This can be achieved
by increasing the overlap between the spectroscopic and photometric surveys. We
show how BAO, WL and RSD contribute to this benefit and also look at some other
survey designs, such as photometric redshift errors and spectroscopic density.
