  The Square Kilometer Array (SKA) has the potential to produce galaxy redshift
surveys which will be competitive with other state of the art cosmological
experiments in the next decade. In this chapter we summarise what capabilities
the first and the second phases of the SKA will be able to achieve in its
current state of design. We summarise the different cosmological experiments
which are outlined in further detail in other chapters of this Science Book.
The SKA will be able to produce competitive Baryonic Oscillation (BAOs)
measurements in both its phases. The first phase of the SKA will provide
similar measurements as optical and IR experiments with completely different
systematic effects whereas the second phase being transformational in terms of
its statistical power. The SKA will produce very accurate Redshift Space
Distortions (RSD) measurements, being superior to other experiments at lower
redshifts, due to the large number of galaxies. Cross correlations of the
galaxy redshift data from the SKA with radio continuum surveys and optical
surveys will provide extremely good calibration of photometric redshifts as
well as extremely good bounds on modifications of gravity. Basing on a
Principle Component Analysis (PCA) approach, we find that the SKA will be able
to provide competitive constraints on dark energy and modified gravity models.
Due to the large area covered the SKA it will be a transformational experiment
in measuring physics from the largest scales such as non-Gaussian signals from
$\textrm{f}_{\textrm{nl}}$. Finally, the SKA might produce the first real time
measurement of the redshift drift. The SKA will be a transformational machine
for cosmology as it grows from an early Phase 1 to its full power.
