  We study the complementarity of weak lensing (WL) and spectroscopic galaxy
clustering (GC) surveys, by forecasting dark energy and modified gravity
constraints for three upcoming survey combinations: SuMIRe (Subaru Measurement
of Images and Redshifts, the combination of the Hyper Suprime-Cam lensing
survey and the Prime Focus Spectrograph redshift survey), EUCLID and WFIRST.
From the WL surveys, we take into account both the shear and clustering of the
source galaxies and from the GC surveys, we use the three-dimensional
clustering of spectroscopic galaxies, including redshift space distortions. A
CMB prior is included in all cases. Focusing on the large-scale, two-point
function information, we find strong synergy between the two probes. The dark
energy figure of merit from WL+GC is up to a factor ~2.5 larger than from
either probe alone. Considering modified gravity, if the growth factor f(z) is
treated as a free function, it is very poorly constrained by WL or GC alone,
but can be measured at the few percent level by the combination of the two. On
the other hand, for cosmological constraints derived from (angular) power
spectra and considering statistical errors only, it hardly matters whether the
surveys overlap on the sky or not. For instance, the dark energy figure of
merit for overlapping surveys is at most ~20 % better than in the disjoint
case. This modest gain can be traced to the fundamental fact that only a small
fraction of the total number of modes sampled by the GC survey (or by the WL
survey) contributes to the cross-correlations between WL and GC.
