Cross correlation surveys with the Square Kilometre Array
  By the time that the first phase of the Square Kilometre Array is deployed it
will be able to perform state of the art Large Scale Structure (LSS) as well as
Weak Gravitational Lensing (WGL) measurements of the distribution of matter in
the Universe. In this chapter we concentrate on the synergies that result from
cross-correlating these different SKA data products as well as external
correlation with the weak lensing measurements available from CMB missions. We
show that the Dark Energy figures of merit obtained individually from WGL/LSS
measurements and their independent combination is significantly increased when
their full cross-correlations are taken into account. This is due to the
increased knowledge of galaxy bias as a function of redshift as well as the
extra information from the different cosmological dependences of the
cross-correlations. We show that the cross-correlation between a spectroscopic
LSS sample and a weak lensing sample with photometric redshifts can calibrate
these same photometric redshifts, and their scatter, to high accuracy by
modelling them as nuisance parameters and fitting them simultaneously
cosmology. Finally we show that Modified Gravity parameters are greatly
constrained by this cross-correlations because weak lensing and redshift space
distortions (from the LSS survey) break strong degeneracies in common
parameterisations of modified gravity.
